otes on Practical 
Mechanical Drawing 



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as a preliminary to copyright protec- 
tion has been found. 

Forwarded to Order Division -^^-i-^^^/.^^.^l. 



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(6, i, 1906—2,000.) 



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Qass. 
Book 



JAru 



NOTES ON 

PRACTICAL MECHANICAL 

DRAWING 



WRITTEN FOR THE USE OF THE STUDENTS IN 

GENERAL ENGINEERING DRAWING 

IN THE UNIVERSITY OF 

ILLINOIS 



VICTOR T. WILSON 

PROFESSOR OF ENGINEERING DRAWING AT 

THE PENNA STATE COLLEGE 

AUTHOR OF 

FREE-HAND PERSPECTIVE AND FREE-HAND LETTERING 



FIRST EDITION — FIRST THOUSAND 



PUBLISHED BY 

THE AUTHOR AT STATE COLLEGE, PA. 

NINETEEN HUNDRED AND SEVEN 



^^ 



<.'^ 



>^ 



t LIBRARY of OONGREsi 
Two Copiss Recesvae 

JAN 27 1908 

CLASS XXc. m, 

COPY B. 



Copyright, 1907 
By Victor T. Wilson 



'ffice. 



^ ^08 




ILLINOIS printing COMPANY 
DANVILLE, ILLINOIS 



PREFACE. 

The following book is a collection of notes upon practi- 
cal mechanical drawing, originally the subject matter of a 
course of lectures, and was prepared to meet the needs of 
the students in the course in General Engineering Drawing 
in the University of Illinois. 

It contains material not hitherto discussed but casually 
in existing books on drawing, notably, the treatment of 
sections, the arrangement and development of a set of 
working drawings, and machine sketching. 

Attention is called to the fact that the book makes a 
long stride in advance of previous methods of teaching the 
subject. Formerly, and even to-day, in many colleges the 
elementary training is accomplished through line exercises 
and geometrical dravving. These are here reduced to a 
minimum, and practical problems take their place. 

It is the author's belief, substantiated by experience, 
that the students' faithful adherence to minute directions 
as to methods of work, insures a ready grasp of the subject. 
And this is why methods are given such expanded treatment. 
It is also counting a great deal upon the student to expect 
him to grasp and apply all the practical points given, but 
in the past, this confidence has not proven vain, and by 
using practical problems from the beginning it has been 



vi Preface 

possible to help him to do this and to keep him interested, 
as he never is in uninteresting geometrical figures. The de- 
parture is not altogether new, however, for the same progress 
is being paralleled in all manual training work. 

The book is not yet complete. It still lacks a set of 
graded exercises upon working drawings and sketching, and 
a few illustrative examples. The elementary principles of 
orthographic projection are also left out, as they form the 
subject of a series of lectures with home exercises, intended 
to parallel the working drawings. 

The author will be glad of any suggestions leading to a 
perfection of his idea. Quotations have been here and there 
been made from standard works upon drawing, and acknowl- 
edgement has been made where such has been done. The 
author wishes, in closing, to express his appreciation of the 
pains-taking work of Mr. C. L. McMaster, as shown in the 
illustrations, most of which were made by him. And not 
a little help was obtained from him, also, in the subject 
matter and in its arrangement. 
Urbana, III., Sept. 1, 1907. 



INDEX 

CHAPTER I. 

STRAIGHT LINE DRAWING. 

Sec. Page. 

1. Definition of drawing 1 

2. Exercise No. 2 3 

3. General directions with regard to preliminary steps 3 

4. Detailed directions for Exercise No. 1 7 

5. General directions in regard to inking 7 

6. Detailed directions for inking Exercise No. 1 9 

7. Detailed directions for penciling and inking Exercise No. 2 . . 10 

8. Detailed directions for penciling and inking Exercise No. 3 . . 10 

9. Detailed directions for penciling and inking Exercise No. 4. . 12 

10. Detailed directions for penciling and inking Exercise No. 5 . . 14 

1 1 . General directions 14 



CHAPTER II. 

CURVES AND STRAIGHT LINES COMBINED AND SECTIONS. 

12. Handling of the compass, dividers and bows 17 

13. General directions for the treatment of Exercises No. 6 to No. 

9, inclusive 22 

14. Special detailed directions for drawing and inking Exercise 

No. 8 26 

15. Special detailed directions for drawing and inking Exercise 

No. 9 ^ 28 

16. Detailed directions for penciling and inking Exercise No. 10. 28 

17. Detailed directions for penciling and inking Exercise No. 11 . 31 

18. Detailed directions for penciling and inking Exercise No. 12. 31 

19. Further points about drawing materials and instruments. ... 34 

20. Sectioning 41 

21. Some practical points about sectioning 49 

22. Some practical points about and the care and handling of 

drawing instruments 55 

23. Exercise No. 13 Sectioning 67 

24. Exercise No. 14 Sectioning 67 

25. Exercise No. 15 Sectioning 67 

26. Exercise No. 16 Sectioning 69 



viii Index 

CHAPTER III. 

Sec. IRREGULAR CURVES AND GEOMETRICAL DRAWING. Page. 

27. Irregular curves 70 

28. System in penciling and inking drawings 74 

29. Geometrical drawing 79- 

30. The conies 87 

31. To draw an ellipse by the focii method 88 

32. To construct an ellipse by the method of the trammel. ...'... 90 

33. To draw an ellipse by the aid of the major and minor auxiliary 

circles 92 

34. To draw an ellipse approximately with the compass. 92 

35. To draw a parabola by means of the focus 95 

36. To draw a parabola by means of its envelope 95 

37. To draw a hyperbola by means of its focii 97 

38. To draw a hyperbola, given the two asymptotes and any point 

on the curve . 99 

39. To draw a hyperbola by the rectangle method 99 

40. The cycloid * 100 

41. To construct the cycloid 101 

42. To draw the epicycloid ! 103 

43. To draw the hypoc^'-cloid 103 

44. Geometrical definitions, terms, etc 104 

CHAPTER IV. 

WORKING DRAWINGS. 

45. The difference between 1st and 3rd angle projection 106 

46. The helical curve and the screw thread 107 

47. The drawing of hexagonal and square-headed bolts 118 

48. Orthographic projection and working drawing 124 

49. Of what a set of working drawings is composed 125 

50. The development and arrangement of working drawings 128 

51. Dimensioning 137 

52. Working drawings may violate the rules of orthographic pro- 

jection 149 

53. Relative value of tentative and exact processes 152 

54. Checking drawings 153 

55. Conventions in common use in working drawings 154 

56. Tracings 158 

CHAPTER V. 

MACHINE SKETCHING. 

57. Machine sketching 159 

58. Blue print process and reproduction 173 



Straight Line Drawing 



CHAPTER I. 
STRAIGHT LINE DRAWING. 

1. Definition of drawing. 

Drawing is the art or science of recording a person's im- 
pressions about things by more or less accurate suggestion 
of form. All drawings may be divided into two general 
classes. (1). The drawings of objects as viewed at a finite 
distance. (2). The drawings of objects as viewed at an 
infinite distance. 

The first of these is called perspective. The point 
of view at a finite distance is called the center of projection. 
It is as if the eye were at the point and the drawing of the 
object was made upon a transparent plane placed between 
the latter and the center of projection, that is, projected 
upon it from this center by lines from the center passing 
through all points of the object. It is a kind of drawing 
that is found in pictures. 

In the second class the center of projection or the eye 
is theoretically moved to an infinite distance, that is, the 
projecting lines from the object to the plane become paral- 
lel. This, in a certain form of drawing, is what is called 
orthographic projection. 

Now things are constructed and manufactured through 
the aid of drawings that are made according to the princi- 
ples of the second kind mentioned, or orthographic projec- 
tion. They may be made free-hand, that is by sketches, or 
they may be made by careful mechanical drawings; in the 

(2) 



Notes on Practical Mechanical Drawing 



more careful and exacting work, they are ahvays made in 
this way. 

A mechanical drawing used for the purpose of construc- 
tion then, consists of one or more views made according to 
the principles of orthographic projection; in addition to 
which the sizes of parts are clearly set forth by dimensions 
with accompanying dimension lines and arrow heads to 
show their limits. 

No matter how simple is the subject to be constructed, 
an accurate and comprehensive and unmistakable drawing 
should be made of it. The test of a good working drawing 
lies in the fact that the workman can make nothing out of 
the facts contained thereon than what was intended by the 
draftsman. The entire meaning should be clear beyond the 
shadow of a doubt. 

To choose the number of views that this may be at- 
tained, to put on the dimensions w^hich the workman will 
need in making the subject is the problem of the draftsman. 
The needs of the Avorkman should be constantly in his mind. 



Exercise No. 1 







Straight Line Drawing 3 

2. Exercise No. 1. 

This a perspective sketch of a form to be made by a 
workman in wood or metal. From this sketch construct 
a plan, side view and two end views, and put on them the 
dimensions shown. The sketch shows just the dimensions 
required and their place, and also the relative distance from 
the views at which the dimensions should be placed in the 
working drawing. 

3. General directions with regard to preliminary steps. 

Tack the paper by the upper left hand corner, then 
with the T sq. head against the left hand edge of the board, 
swing the paper into line with its upper edge. " Next, draw- 
ing it tight, put in the tack at the upper right hand corner, 
and then, stretching from the center out, put in the lower 
two tacks. Sometimes it is best just to clip the corners of 
the paper under the thumb tack head, in this case a very 
small amount of stretching can be effected by heading the 
point of the tack, as it is pushed in, slightly away from the 
corner to be tacked. 

Drawings have frequently to be taken up from the 
board and reset again. When this is needed short horizon- 
tal lines drawn with the T sq. on each side of the sheet and 
extending onto the board are convenient for guiding the 
sheet into the same place it held on the board at first. 

The border line for all plates, unless specially arranged 
for, is to be ^ inch from the edge of sheet. 

Hold the T sq. with the hand over the head or by the 
blade very close to the head. The advantage in the latter 
method is that by means of the fingers held at the upper 



4 Notes on Practical Mechanical Drawing 

and lower edges of the blade, it can be made to creep by- 
short distances up and down the board. 

Keep the T sq. always against the left hand edge of the 
board and always use, for working, only the upper edge of 
the blade. Sometimes large T sqs. are made tapering away 
from the head. When so made, the taper is always upon 
the under side. 

Keep the triangles convenient to the T sq. always, that 
is, when not using, move to the right along the blade or 
away from the blade upward, but so that when needed again 
they can be drawn into place against the T sq. blade with 
the minimum of effort. 

In using the triangle against the T sq. blade, observe 
the following proceeding. Adjust the T sq. first, with the 
right hand bring the triangle into place, and hold with the 
fingers of the left hand while the ball of the same hand holds 
the T sq. blade in place. The triangle can be thus moved, 
if desired, along the blade in easy stages _as for section 
lining, etc. 

Rule vertical lines upward against the left hand edge 
of the triangle placed as just described. Do not draw to 
the extreme point of a triangle or to the point it touches 
an adjacent ruling edge against which it may be resting, for 
the sharpness of the angle cannot be depended upon. 

Rule all lines in pencil as shown in Fig. 1. This direc- 
tion is given now in order that the habit may be formed 
preparatory to the use of the ruling pen, which requires 
this treatment. 

Remember, as a final direction, that points for locating 
lines should be as far apart as possible, while lines used in 



Straight Line Drawing 



U/^/f'ofc}' secf/'o/?. 







Ouf-//he-. 



2s- 



locating points should cut each other as nearly as possible 
at right angles. 

The lead pencil may be sharpened in one of two ways, 
by a long, tapering, round point or by a double-edged chisel. 
Cut the wood back for at least f of an inch from the end and 
leave from \ to f of an inch of lead exposed. Taper both 
down continuously to, if possible, a slightly concave form. 
The advantage of a tapering point is that it holds its sharp- 
ness for a longer time, and again, the point is not thick 
enough to cover up the work in hand or to mislead as to 
where the lead is marking. 

The double-edged chisel should not be quite as wide 
across as the lead is thick, but reduced somewhat, say to | 
the diameter. A penknife for the wood and emery paper 
or a file for the lead will give the desired results most 
rapidly. 

If the double-edged chisel is used it should only be for 
straight away lines, not for laying off measurements from 
the rule or scale. The round pointed form may be used 
either for picking off measurements from the rule or scale 



6 Notes on Practical Mechanical Drawing 

or to draw lines. If a chisel form is used for the lines, a 
pencil sharpened to a round point should be kept handy for 
picking off measurements. 

In holding the pencil, keep it nearly perpendicular to 
the paper; if drawing lines with the round point, acquire 
the habit of slowly twirling the pencil during motion, so that 
the point will be worn down in a conical shape, and not 
irregularly. 

Clean, firm lines, uniform in thickness and blackness 
both in penciling and in inking, are the kind which should 
be cultivated. The draftsman is known quite as well by 
the character of his penciling and construction as by his 
final inked drawing, carelessness and irregularity in the 
former is quite as surely to be repeated in the latter. 

Avoid drawing superfluous lines, lines overrunning their 
proper limits or lines that are not to be inked. If accidental 
errors are made, correct them with the eraser at once. The 
neat draftsman is he who does his work with the least use of 
the pencil and eraser. Lines also which are to be dotted, 
in final drawing, should be dotted in pencil so that no mis- 
take is made when inking. Wherever possible, locate the 
extremities of a line by the scale before drawing it, which 
is facilitated by placing the scale against the ruling edge. 

After making an erasure, clean off the particles of dirt 
that are loose on the paper, for they interfere with the 
smooth and proper action of the other tools. This is a par- 
ticularly important direction to observe preparatory to ink- 
ing and when any alterations are made during inking. Too 
much care cannot be observed in freeing the paper and all 
tools from the dirt particles, for they are quite apt to get 
into the pen and give trouble. 



Straight Line Drawing 7 

4. Detailed directions for Exercise No. 1. 

Draw the plan view first, laying out the center line, 
scaling the length over all, the width of each end, and then 
enclosing by lines. Draw the elevation next and then 
either end. After the views have been drawn put on the 
dimension lines, limiting lines, and arrow^ heads, lastly the 
dimension figures. The drawing is then ready to be inked. 

5. General directions in regard to inking. 

To put ink into a right line pen, hold the pen approxi- 
mately horizontal with the kind of holding usually given to 
a wTiting pen. Hold the bottle down with two fingers and 
with two others lift the cork out and touch the quill end 
between the nibs of the pen, to let the ink run in, and do 
this over the bottle, for obvious reasons, corking it securely 
when through. If the nibs of the pen get ink on the outside, 
wipe oft' with a rag. 

To hold the pen for ruling lines, raise the handle from 
the previously described position until it rests at or slightly 
in front of the second joint of the first finger. Have the end 
of the first finger just above the adjusting screw on the flat 
part of the nib, the thumb just opposite this, and the second 
finger touching the pen between the first finger and the 
thumb and just below them to steady it from any tendency 
to turn. Hold the pen always perpendicularly to the paper, 
steadying the hand against the ruling edge with the last 
finger or the last two. 

The weight o'f the pen alone should be sufticient to 
make the desired line. If it does not, after trying a few 
times on a piece of trial paper, clean out and refill. 

' Do not exert any pressure of the pen against the ruling 



8 Notes on Practical Mechanical Drawing 

edge, as it will tend to close the nibs. Make all lines by a 
continuous motion of the pen. Do not stop on a line to see 
where the rest of the line is to go. If it is absolutely neces- 
sary to stop in any case, even for a moment, lift the pen 
from the paper. Also, when stopping in this way, take the 
further precaution to move the ruling edge away from the 
wet line. 

When requiring refilling, clean the pen out thoroughly 
so that no ink remains either upon the inside or outside of 
it. It is well to cultivate the habit of doing this early, 
making it invariable, for a pen clogged with ink is likely to 
give trouble. Devices for readily opening a pen to facilitate 
cleaning have been much advertised, and some are quite 
meritorious. However, they have not yet become indis- 
pensible to the experienced draftsman, for the cleaning can, 
with a little practice, be done very effectively without their 
aid. Use the nails of the thumb and first fingers succes- 
sively, covered by one thickness of rag, and it will be found 
easy to clean one half of a blade with one finger and the 
other half with the other, and the remaining blade by turn- 
ing the pen over and repeating the operation. Four wipes 
generally clean sufficiently and with perhaps no more ex- 
penditure of time than by the aid of the opening devices 
mentioned. 

If the pen gives any trouble in marking at any time it 
is safest to empty, clean and refill. 

The weight of an ink line on a drawing should be such 
that it will show clearly the form within the maze of dimen- 
sion lines, etc., that it will blue print readily, giving an 
equally clear impression throughout, and that all annoyance 
is removed, due to the likelihood that the line will break 



Straight Line Drawing 9 

through any obstructed flow of the pen. In Figure 2 are 
shown suitable conventions to use on a drawing, as well as 
the proper weight of line.* 

It is highly important in the very beginning to cultivate 
a uniform line throughout. It takes experience and a 
trained eye to do this accurately and at the same time 
unconsciously. 

6. Detailed directions for inking Exercise No. 1. 

Rule the horizontal outlines of all the views first, begin- 
ning at the top and going down. Rule the vertical outlines 
next, including dotted lines or invisible edges, then the 
oblique lines. Rule the limiting and dimension lines next, 
and lastly put in arrow heads and dimension figures in the 
order named. 

A drawing should be cleaned after all inking is finished. 
A very soft rubber will clean dirt very well, but it is hardly 
sufficient for superfluous pencil construction lines. Care 
should be exercised in erasing the latter with a harder eraser 
on account of injuring the ink lines, for much erasing will 
spoil the quality of any ink line. 

In erasing, hold the paper firmly with one hand while 
the stroking of the eraser is in the direction away from it, 
or else hold with the thumb and forefingers of one hand 
opposed to each other and move the eraser between them, 
the whole object being to take the strain off the thumb 
tacks. 



*NoTE. — Sometimes in fine careful drawings dotted lines can be made to appear 
equal in thickness to the solid lines, but to do this they have to be made actually thinner. 



10 Notes on Practical Mechanical Drawing 

7. Detailed directions for penciling and inking Exercise 

No. 2. 

Draw the plan view first, laying out the center line^ 
scaling the length over all, and the width of the view. Next,. 
lay off the shorter horizontal distances, preferably upon the 
center line, marking continuously from the scale, then the 
vertical measurements, either side of the center line at the 
points marking the horizontal distances. Line in the view^ 
horizontal lines first and then verticle lines. 

Lay out the elevation in the same manner as the plan. 
Put on the limiting lines, dimension lines, arrow heads and 
figures in the order named. 

In inking, rule the horizontal outlines of all the views, 
first, beginning at the top and going down. Rule the ver- 
tical outlines next, including dotted lines or invisible edges.. 
Rule the limiting and dimension lines next and lastly put in 
arrow heads and dimension figures in the order named. 

8. Detailed directions for penciling and inking Exercise 

No. 3. 

Draw the plan view first, laying out center line, scaling 
the length over all and the width of each end, then enclosing 
by lines. Draw the elevation next, and then either end. 
After this put on the dimension lines, limiting lines, and 
arrow heads, lastly the dimension figures. 

In inking, rule the horizontal lines of all the views first,, 
beginning at the top and going down. Rule the vertical 
outlines next, finally the oblique lines. Next, rule the lim- 
iting lines and dimension lines, then put in arrow heads and 
dimension figures. 



Straight Line Drawing 



11 



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12 



Notes on Practical Mechanical Drawing 
Exercise No. 3 



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9. Detailed directions for penciling and inking Exercise 
No. 4. 

Draw the plan view first, laying out the center line, 
scaling the length over all, and the width of the view. Next, 
lay off the shorter horizontal distances, preferably upon the 
center line, marking continuously from the scale, then the 
vertical measurements, either side of the center line at the 
point marking the horizontal distances. Line in the view, 
horizontal lines first and then vertical lines. 

Lay out the elevation in the same manner as the plan. 
Put on limiting lines, arrow heads and figures in the order 
named. 

In inking, rule the horizontal outlines of all the views 
first, beginning at the top and going down. Rule the ver- 
tical outlines next, including dotted lines or invisible edges. 
Rule the limiting and dimension lines next, and lastly put 
in arrow heads and dimension figures in the order named. 



Straight Line Drawing 



13 




14 Notes on Practical Mechanical Drawing 

10. Detailed directions for pencilling and inking Exercise 

No. 5. 

Draw the plan view first, laying out center line, scaling 
the length over all and the width of each end, then enclosing 
by lines. Draw the elevation next, and then either end. 
After this put on the dimension lines, limiting lines and 
arrow heads, lastly the dimension figures. 

In inking, rule the horizontal lines of all the views first, 
beginning at the top and going down. Rule the vertical 
outlines next, finally the oblique lines. Next, rule the di- 
mension and limiting lines, then put in arrow heads and 
dimension figures. 

11. General directions. 

Detailed directions were given for laying out and for 
inking exercises Nos. 1 to 5 inclusive. This was done because 
-method of execution is important, a certain procedure being 
economical of time and effort in the drawing and more likely 
to result in accuracy. It is now time to. discuss this matter 
a little more minutely. 

The preceding exercises show a symmetry upon a center 
line. It is best to regard this symmetry in the construction 
of the drawing, that is, to lay out the main center lines of 
forms first and then measure either side of these center lines, 
saving a duplication of measurements. 

Again, to avoid drawing superfluous lines, it is best to 
mark first the sizes of areas that are to be enclosed with 
lines, these sizes will aid in stopping the lines at the 
right places. Again, always size and enclose the larger 
areas first, the smaller features are then most likely to be 
Tight, and they are, moreover, better seen in their proper 



Curves and Straight Lines Combined, and Sections 15 



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16 Notes on Practical Mechanical Drawing 

places, when the larger things upon which they depend are 
there with which to compare them. It is a part of the train- 
ing of the draftsman to acquire the judgment necessary to 
execute a drawing economically of time and effort. Such 
details as have been given will hereafter be omitted and only 
those processes outlined which differ from the preceding. 



Curves and Straight Lines Combined, and Sections 17 



CHAPTER II. 

CURVES AND STRAIGHT LINES COMBINED, 
AND SECTIONS. 

12. Handling of the compass, dividers and bows. 

There is a difference between geometrical and mechan- 
ical drawing. Geometrical drawing is drawing by the meth- 
ods of geometry, constructing everything geometrically, 
parallel lines, lines at various angles to each other, and so 
on. The geometrical drawing instruments are the compass 
and the straight edge or ruler. All other tools, including the 
dividers, the T sq., triangles, etc., are mechanical drawing 
instruments for accomplishing the same purpose. 

The compass and dividers are similar to each other, but 
the use of the compass should be cultivated more than the 
dividers. The compass is for describing circles and meas- 
uring angles, and also for transferring measurements from 
one place to another. The dividers are used to approxi- 
mately subdivide linear distances and for transferring meas- 
urements from one place to another. It is, many times, a 
more convenient tool for doing these things, and one of the 
habits to cultivate is to minimize the use of the dividers. 
It is an excellent tool in its place, but it is not as safe to 
depend upon as the scale. 

In changing the marking legs of the compass, use care 
to pull or push the attachment longitudinally of the leg, and 
not to twist it or move it laterally, it might strain the 



18 Notes on Practical Mechanical Drawing 

members. The instrument is easily injured, and accuracy 
of action is necessary. 

The needle point of the compass should have a shoulder 
on it to prevent sticking too deep in the paper; it should be 
adjusted to fit the pen attachment and always be kept so. 
In working with the pencil leg then, and as it wears down, 
extend the lead to meet properly the needle point adjust- 
ment. The pencil in the compass should be sharpened 
always to the double-edged cliisel. 

The proper position for the needle point is slightly in 
advance of the marking point, depending upon the degree 
of sharpness and the length of the point. At no time should 
the point more than hold in the paper. And when stuck in 
to this degree, the bisector of the angle of the compass legs 
should be perpendicular to' the line connecting the two 
points. This is very important in making small circles. 

The compass should be held with one hand only, for 
obvious reasons, apparent after experience. To open the 
compass at first, press the thumb and first finger against the 
bevelled partion near the head. To hold the compass when 
opened, control the needle point leg with the thumb and 
third finger, the marking leg with the first and second fingers, 
held, generally, the former upon the outside, the latter upon 
the inside of the leg, so as to move the leg in and out with a 
controlled motion. The tightness of the head should be 
just sufficient to hold the compass in place during use ; such 
an adjustment will not render it difficult to change the angle 
between the legs easily with the fingers as described. 

If the hand is unsteady, it may be found convenient to 
use one hand for putting the needle point in the proper 
center, either by taking hold of the end of the needle point 



Curves and Straight Lines Combined, and Sections 19 

leg or by resting the leg against the finger while putting it 
into place ; the latter is the better way. 

Curves should be drawn continuously and always in the 
same direction, clockwise. In drawing a complete circle, 
start the marking point at the lowest part of the circle, or 
ev^en a little to the right, and it will be found possible to 
swing the whole circle without change of handling, by roll- 
ing the head in the fingers during rotation. It should not 
be necessary to change the handling at any time, or the 
position of the hand or the instrument. Held correctly, it 
should always be ready for drawing. It is a very common 
fault to hold the compass with two hands. 

Further, it should be held so that the head is slightly 
in advance of the marking point in the direction in which 
the curve is being made, to aid the marking point to remain 
in contact with the paper. But do not bear any more pres- 
sure on either leg than is necessary to make the curve and 
to keep the needle point in contact with the paper; in ink 
work, the weight of the instrument, as in the case of the 
ruling pen, should be sufficient to make the desired line. 

Do not overlap a circular curve in inking; there is a 
chance of a change of adjustment, and even if this is not the 
case, it is likely a line twice drawn over will spread out, 
making a noticeable junction. 

There is a hairspring attachment put on some com- 
passes and dividers. It has merits in enabling one to make 
a very delicate change of adjustment, but the author thinks 
the value of this feature is very much over estimated, for, 
with experience, comes sufficient skill that, handled as above 
described, the desired adjustments are made more rapidly 
than they could be by a hairspring attachment, taking as it 



20 Notes on Practical Mechanical Drawing 

does two hands for manipulation. Of the two instruments, 
however, the hairspring is of more value upon the compass 
than upon the dividers. 

There is a certain point reached in the spreading of the 
legs of the compass when it is very desirable to bend the 
ends of both the needle point leg and the marking leg at the 
proper joint, always provided, so that both come down per- 
pendicularly to the paper. This point, for a six-inch com- 
pass, is in the neighborhood of a three-inch diameter. It 
is easy to see that if the needle point is inclined to the paper 
appreciably, it will, when swung around, gouge a larger hole, 
and similarly considered, the nibs of the pen attachment 
would not touch the paper together; the outer one might 
rise sufficiently to make a ragged line. 

A lengthening bar is used for circles beyond the capacity 
ordinarily of the compass, but it is an inconvenient thing to 
use, makes an unsteady tool, and if much work is to be done 
on large radii it is well to use a beam compass, built especially 
for this purpose. 

The dividers are held in the same manner as the com- 
pass. If a given distance is to be divided into a certain 
number of equal parts that do not correspond to any scale 
divisions, the dividers can be used to do it by successive 
approximations. In stepping off such equal spaces, the 
tool should be swung alternately over and under, so that 
the holding need not be changed, no matter how many suc- 
cessive distances are to be made. Moreover, but slight 
pressure should be exerted on the tool, so that the points 
make no noticeable hole in the paper. To locate a pick of 
the divider leg for further reference, put a small free-hand 
circle about the point, not much over a sixteenth of an inch 



Curves and Straight Lines Combined, and Sections 21 

in diameter; this calls attention to the region in which the 
point Hes. Large holes in a drawing are unsightly and are 
really inaccurate. Sometimes, also, an ink line going into a 
large hole will give rise to a blot. 

The bow instruments are very convenient, small and 
accurate tools for doing the same kind of things that the 
compass and dividers will do. The adjustment of needle to 
marking point in the bow pen and pencil should be even 
more carefully made than in the compass, because of the 
small circles for which they are used. On account of their 
accuracy and positive adjustment, the bows in practical 
work are used wherever they can be, but since there is 
nothing distinctive to be learned about them, the beginner 
is advised rather to favor the use of the latter so that he may 
get as much practice with them as possible, and acquire the 
proper handling, which does not generally come naturally 
at first. 

The small circles upon commercial drawings are not 
infrequently omitted in pencilling, only the centers being 
located, but a caution is extended to the beginner not to 
resort to this form of short-cut for obvious reasons, but to 
pencil in everything very completely and accurately. The 
omissions of construction should be left to the judgment of 
the skillful draftsman. 

A caution is also here extended regarding the bow 
dividers. Their particular use, in fact, their only econom- 
ical use, is to lay off a succession of equal measurements. 
It is so much trouble to set them to transfer a single meas- 
urement that the dividers are better for this purpose. But 
since, if any mistake is made in the setting, it will increase 
the error by arithmetical progression, as successive meas- 



22 Notes on Practical Mechanical Drawing 

urements are laid off, it can be seen that the scale is after all 
the safer tool if it is possible to use it. The value of the bow 
dividers is apt to be much over estimated. It could be left 
out of the ordinary set of instruments without any serious 
drawbacks. 

As a practical point in handling, it should be noted that 
if a decided change is to be made in the adjustment of the 
bows, it is less wear on the instrument and also more eco- 
nomical of time to take the strain off the legs by pressing 
them together with one hand while the thumb-screw is 
twirled around with the other until near the proper adjust- 
ment. 

13. General directions for the treatment of Exercises No. 6 
to No. 9, inclusive. 

Draw the center lines first and next the centers of arcs 
and curves tangent to straight lines ; that is, make the out- 
line or contour forms (except in the case of very small curves 
or fillets, as in Exercises Nos. 8 and 9) determined by the 
curves to which they are tangent. In construction, the 
exact location of these centers may be very important. 
After the centers are located and the curves drav/n, enclose 
the remaining part of the views by the straight lines, and so 
on to the finish. 

It is important to be exact in the tangency of curves to 
straight lines and of curves to each other ; therefore observe 
that the marks in the paper made by the needle point centers 
are as small as possible. 

The centers for all arcs, other than very small ones like 
fillets, should be indicated by at least two center lines cross- 



Curves and Straight Lines Combined, and Sections 23 

ing each other at right angles at the center, say J of an inch 
long. 

In inking, it is also important to observe tangency, and 
since it is found practically very difficult to copy a pencil 
line in ink accurately, hence more difficult to make a curve 
tangent to a straight line than it is to make a straight line 
tangent to a curve, it is customary to ink in all circular arcs 
and circles first, going from the smaller curves to the larger 
ones, so as to be sure of the capacity of the bow pen to do 
its part. 

A word is here in order about dotted lining. Dotted 
lines can be made quite explanatory of forms and they can 
also be made quite obscure, depending upon the treatment. 
The thickness of a dotted line should be no greater than that 
of the solid outlines, in fact, it is well to make it slightly 
lighter, for the short dots are likely each to be thicker than 
a continuous line made with the same setting of the pen. 
Even in the absence of this (in the case of fine lines) the 
dotted line may attract more attention than a solid line and 
should be made lighter to offset it. 

Again, a dotted line is not ideally composed of dots, 
but of short, uniform and evenly spaced strokes. The uni- 
formity of dotting is a thing which makes it look well on a 
drawing. Dotted construction should look intelligible al- 
ways. To effect this, several points need be observed: 

(a). The angles of sharp corners should be connected 
strokes, (b). Where the dotted line crosses solid lines, and 
is not related to them by identity of form or material, the 
dots should not stop at, but may cross, these lines, (c) . Where 
dotted lines properly end at solid lines, the dots should touch 
the lines, (d). In the dotted lines in either of the above 



24 



Notes on Practical Mechanical Drawing 




Curves and Straight Lines Combined, and Sections 25 



,«y>l«>««WN.^(^^.»-.-.-.*-,t>A 





4 ^~S / "^ \ 





'^ 'U* \/ / 








ii___.i2:.^l_„/ 



26 Notes on Practical Mechanical Drawing 

cases, the dots marking the angles, or those crossing soHd 
lines or meeting to end at solid lines, can well be made longer 
than the dots of the rest of the line, even by twice the length- 
Dotting, in brief, should clearly define the forms by accentu- 
ating w4th larger dots the salient things to be brought out. 
The detailed directions for laying out and inking any 
one of the preceding exercises apply also equally well to any 
one of the Exercises Nos. 6 to 9. But some special direc- 
tions connected with them are here introduced. 



14. Special detailed directions for drawing and inking Exer- 
cise No. 8. 

For the sake of clearness, we will call the front view of 
this a view looking along the rocker shaft, and the end view 
the one looking into the fork. 

This is a form illustrating the advantage, which will be 
more apparent with greater experience, of developing parts 
of several views simultaneously. The front view, including 
the split collar and what is below, is best drawn first; that 
which is above the split collar, including the tightening bolt, 
-should be drawn in the end view first. 

The views should be drawn at first ignoring the small 
rounded edges or fillets, these put in afterwards by carefully 
located centers, and left perfectly clear in form. 

Note that the bolt should have two rectangular faces 
of the head and nut horizontal planes. The bolt head and 
nut as shown are not what are called finished forms. They 
are so drawn to be easy. The finished forms will be dis- 
cussed later. 



Curves and Straight Lines Combined, and Sections 27 



Exercise No. ? 



iibo^e 



!G 



'eol^ 



3hovv 



cS'ott-ed. 






^ bolfliecjJl 



• t ^ 



J V)lcO 



&how bol 











28 Notes on Practical Mechanical Drawing 

15. Special detailed directions for drawing and inking Exer- 

cise No. 9. 

Let us call the front view the one looking along the 
shaft, and the side view the one looking transversely of the 
shaft. The front view should be drawn first. As before 
stated, it is easier to draw a straight line tangent to a circle 
than it is to draw a circle tangent to a straight line. 

Where, as in Exercise No. 8, cylindrical forms show 
ends in both views, then it is desirable to develop parts of 
both simultaneously, drawing the component parts in that 
view first which is the more easily drawn. 

The key- way should be drawn after the circles are 
struck, and, of course, in the front view first. 

Note the conventional method of showing a broken 
shaft in side view, as given by the small detail to the right 
of Exercise No. 9. The curved part is sometimes made with 
the curved rule, but since it is to represent an irregular 
break, it may Vvdth equal propriety be represented by a free- 
hand pen line, not too ragged. The sectioning, or conven- 
tional method of showing the cut surface, should in all cases 
be ruled in by equally spaced lines somewhat lighter than 
the general outlines, and in the case of this exercise, slightly 
less than one-sixteenth of an inch apart. 

16. Detailed directions for penciling and inking Exercise 

No. 10. 

This is an exercise in the tangency of circular arcs. It 
is a cross section of a P. R. R. standard 100 lb rail. Draw 
the view as sketched making it carefully full size, using the 
scale for laying out the sizes. 



Curves and Straight Lines Combined, and Sections 29 



Exercise No. 9 




30 



Notes on Practical Mechanical Drawing 



Draw the vertical center line first, then the centers for 
the arcs designating the web, then the crown of the rail, and 

Exercise No. 10 




the base and so on, locating centers in the penciling carefully 
by free-hand circles around the intersections of the con- 
struction lines. Put the dimensions on practically where 
shown on the sketch. 



Curves and Straight Lines Combined, and Sections 31 

When ready to ink, put in the small arcs ^^ith the bow 
pen, then the larger with the compass and lastly the straight 
lines. Show the plane of the section by regularly spaced 
Hnes at 45° to the horizontal and about Vie ^^ ^^ i^ch 
apart at the very least, the weight of line to be slightly 
lighter than the outline. 

17. Detailed directions for penciling and inking Exercise 

No. 11. 

This is an exercise in the tangency of circular arcs. It 
is a small detail of a riveting machine, a flange for outlet 
and inlet pipes; the pipes screw into the holes shown. 
Draw the views as sketched ; making it carefully full size, 
using the scale for laying out the sizes. 

Draw the main center lines of the upper or plan view 
first, continuing the vertical one down to the elevation. 
Next draw the minor center lines of the plan, then close in 
the plan, smaller circles first then larger and the straight 
lines last. DraAV the elevation from the plan, making the 
tipper and lower horizontal limiting lines first, then pro- 
jecting dow^n from the plan. Put the dimensions on practi- 
cally where shown on the sketch. 

When ready to ink, put in the small arcs with the bow 
pen, then the larger with the compass, and lastly the straight 
lines. Put in the dimension lines and figures the very last. 

18. Detailed directions for penciling and inking Exercise 

No. 12. 

This is an exercise in the tangency of circular arcs. It 
is a stop lever. Draw the proper views from the sketch, 



32 Notes on Practical Mechanical Drawing 




N 



^^ 



Curves and Straight Lines Combined, and Sections 33 

making them carefully full size, using the scale for laying 
out the sizes. 

Draw the horizontal and oblique center lines of both 
views first. Next draw the central boss and left hand end 
of the lower view or elevation. Then draw the fork of the 



Exercise No. 12 




plan view an(i project down to the elevation. Finish the 
elevation, then the plan. Put the dimensions on practically 
where shown on the sketch. 

When ready to ink, draw^ the circular arcs first, then the 
horizontal, vertical and oblique lines in order. Put in the 
dimension lines and figures the very last. 



34 Notes on Practical Mechanical Drawing 

19. Further points about drawing materials and instru- 
ments. 

If you want to do good work, you should have good 
tools. If it happens that an excellent workman does good 
work with very indifferent tools, it only means that his work 
is done in spite of, not by the aid of, his poor tools. It is 
not to be doubted that the poor ones are more or less of a 
hindrance. Nor is it the opinion of the writer that beginners 
should have any poorer instruments for work than the ex- 
perienced man upon the score of his inexperience, and the 
likelihood that he will spoil his first tools by improper hand- 
ling. A student's first lesson to learn and a teacher's first 
duty is to teach the proper use and care of tools. With this 
lesson learned, it should be possible for the beginner to work 
safely with the best appliances. 

Again, the inexperienced workman, of whatever craft, 
will bear witness to the statement that the very best appli- 
ances are never too good, better tools are continually being 
constructed and go into immediate use. It is the purpose 
now to sa}^ something about the different tools and their 
proper care and handling. 

Drawing hoards: The best drawing boards are made 
of well seasoned pine, of uniform grain, narrow strips glued 
together, the whole being finished at the two opposite ends 
at right angles to the strips by narrow pieces tongued and 
grooved and glued to the board, to prevent warping. Fig. 3 
shows one of these boards. 

In large boards, of first class construction, battens are 
favStened to the back of the board so as to permit of expansion, 
and contraction of the board with changing temperature, but 
not of warping. This is effected by fastening a batten. 



Curves and Straight Lines Combined, and Sections 35 



rigidly at one point near the middle, and at two or more 
other points by screws rigid in the board but working in 
slots in the batten. In order to still further lessen the tend- 
ency of the board to warp, saw cuts or grooves are made 
about two inches apart, longitudinal of the strips of which 

Fig. 3 






d 



m 




the board is constructed and of a depth of about half the 
thickness of the board. 

It is not absolutely necessary that all four edges of a 
board should constitute a true rectangle, they ought to be 
straight. Only one edge of a board, the left hand edge, 
should be used upon which to rest the T sq. head, the tri- 
angles should be used for vertical lines. 

The under side of a battened drawing board may con- 
veniently be used to cut paper on, but it should never be 
done on the w^orking side, and care should be exercised that 
the working side and the edges of the board be kept clean 
and in all respects in good order. 



36 Notes on Practical Mechanical Drawing 

Tee squares are made in various forms. They should 
be of well seasoned wood of uniform grain. The blade may 
be sunk in the head or screwed on top and glued. A frequent 
source of trouble in T sqs. is that the part of the head just 
under the blade swells under the action of the moisture in 
the glue when it is made, becomes set, and causes the head 
to rock against the edge of the board when in use. The 
bulge in the head can be seen by placing a straight edge 
against it. An excellent form of T sq. is made of mahogany, 
with a very narrow edging of ebony. The latter is particu- 
larly hard, it relieves the edge by its strong contrast with 
the color of the paper. Sometimes a celluloid edge is used. 
This seems to have growing favor because of its transpar- 
ency, permitting partial sight of the work underneath. If 
T sqs. are large, they are tapered as before micntioned, so that 
the upper edge is the only one that can be and which always 
should be used. 

Some T sqs. are made with a swivel head so that the 
angle of the blade can be adjusted and they have their value 
sometimes. It may be said that one should be in a well 
equipped drafting office, but that for ordinary use it is not 
necessary. Steel T. sqs. are made but are not favorites with 
draftsmen because of their weight and the danger of injury 
to the drawing by denting, etc. 

Triangles are made of the same materials as the T sqs., 
solid triangles, however, are not good as they will warp. Tri- 
angles are made also of vulcanized rubber and of celluloid. 
The former have the advantage of contrasting well with the 
color of the paper, but they have the disadvantage of being 
non-absorbent, consequently they transfer dirt from one part 
of the drawing to another and smear it. 



Curves and Straight Lines Combined, and Sections 37 

The inside edges of a triangle may have depressions cut 
in them to faciHtate picking up from the paper. This may- 
seem an advantage to some ; it is certainly no drawback. 

A 30° and 60° triangle and a 45° triangle are the only 
ones in common use except those especially made for me- 
chanical lettering. Some other angles may be struck by 
using the triangles together and adding their angles, 15°, 75°, 
etc. The accuracy of triangles is important, they may be 
proved by reversing operations with them, means hardly 
worth while describing at length, or by using a protractor, 
to be shortly described. 

Paper for drawing upon comes of various kinds and 
quality, suited more or less to different kinds of drawing. A 
moderately heav}^, smooth hard surface is to be desired for 
mechanical drawings. A yellow^ or manilla paper is much 
used for pencil drawings when the resulting drawing is to be 
traced. It is called detail paper. Bond paper has also come 
quite into use, and it has distinct advantages. The drawing 
is penciled and inked on the paper and from it blue prints 
can be readily made. Paper should if possible never be 
rolled, particularly rolled small as it cannot be satisfactorily 
flattened again. 

Tracing cloth is in almost universal use in drafting rooms 
for permanent drawings, as blue prints can be so readily 
made from it. Either the rough or the smooth side can be 
equally well used for drawing in ink. Frequently the origi- 
nal pencil drawing is made upon the rough side of the cloth 
and inked over. It furnishes a very good surface for this 
purpose. The smooth side is impractical for pencil drawings 
but takes ink like a highly calendared surface. Special 
precautions, wliich will be mentioned shortly, have to be 



3S Notes on Practical Mechanical Drawing 

observed in working upon it. There is but one recognized 
grade and make of tracing cloth, the "Imperial." 

Stretching of paper, as it is called, is resorted to where 
any water color brush work is to be done. It consists of 
pasting the edges to the board and shrinking until it is quite 
taut. It takes a little experimenting to get facility in doing 
this, but every one ought to know how to do it when occasion 
arises, hence the following directions are appended. 

*"To stretch paper tightly upon the board, lay the 
sheet right side up — Avhich side is presumably the one which 
shows correct reading of the water mark when held to the 
light — place a rule with its edge about one-half inch back 
from each edge of the paper in turn, and fold up against it a 
margin of that width. Then thoroughly dampen the back 
of the paper with a full sponge, except on the folded margins. 
Turning the paper again face up, gum the margins with 
strong mucillage or glue, and quickly but firmly press oppo- 
site edges down simultaneously, long sides first, exerting at 
the same time a slight outward pressure with the hands to 
bring the paper down somewhat closer to the board. Until 
the gum sets so that the paper adheres perfectly where it 
should, the latter should not shrink ; hence the necessity for 
so completely soaking it at first. The sponge may be applied 
to the face of the paper provided it is not rubbed over the 
surface, so as to damage it. The stretch should be horizontal 
when drying, and no excess of water should be left standing 
on the surface ; otherwise a water mark will form at the edge 
of each pool." 

The drawing instruments that have already been men- 
tioned, the compass, dividers, etc., constitute the simple 

* F. N. Wilson's Theo. and Practical Graphics, P. 14. 



Curves and Straight Lines Combined, and Sections 39 

universal kit, and probably the majority of draftsmen have 
little else. Of course there are a number of other tools 
made, chiefly for special uses. The use of these is not uni- 
versal, howeA^er, chiefly because the time saved with a 
special tool is usually offset by the time consumed in hand- 
ling and cleaning, for each special tool comes in generally for 
but occasional and brief use. Somewhat similar reasons 
explain why various special attachments to the simple kit 
are not popular universally, like hair spring legs in compass 
and dividers, spring catch ruling pens, miicrometer adjust- 
ment to needle point, etc. 

Beam compasses are instruments to strike large circles, 
consisting of a needle point leg and marking point leg, each 
separate and adjustably mounted upon a bar of metal or 
wood. Every large drafting room is hkely to have one for 
occasional use, but the individual hardly needs to go to the 
expense of one unless its use is demanded frequently. 

Follower pens, in which ' the pen is swivelled in the 
handle, are used to make irregular curves. The pen auto- 
matically adjusts itself properly to the ruling edge. It has 
but occasional use. 

A how pen is made, chiefl}^ for special professions, which 
has a fixed needle point leg with a marking leg sliding freely 
upon it. It is handy for striking a large number of circles 
of small diameter, but it is a tool for that special purpose. 

Dotting wheels are instruments to do what the name 
implies, make dotted lines. They also have occasional use 
but are a trouble to care for and easily get out of order. 

Proportional dividers, consisting of double pointed legs, 
pivoted between the ends, and adjustable so as to give a 
range of relation between the opposite angles formed, are a 



40 Notes on Practical Mechanical Drawing 

very useful tool indeed upon those rare occasions when a 
drawing is merely to be copied to a different size regardless 
of scale. Where scale is to be observed it is not safe as a tool 
nor is it much handier than the scale direct. 

A parallel straight edge is made which replaces the T sq., 
A rule, of the length of the board, is held at the ends by slid- 
ing on a wire cable and moves into parallel positions. The- 
oretically it is excellent but lack of sufficient rigidity is its 
chief drawback in the opinion of many. 

The protractor is a semi-circular disc segment of celluloid, 
bone or brass with degrees marked upon it. The center is 
marked on the straight edge of it. It has use where angles 
have to be struck of varying sizes and other than those the 
triangles can be used for. 

There is a machine on the market known as the Universal 
Drafting Machine, which has very meritorious features. It 
combines the functions of the T sq., triangles and scale and, 
when speciall}^ adjusted, the protractor. 

It consists essentially of two straight edges with scales 
upon them and with a common point of attachment. They 
can be set rigidly at any angle to one another and the whole 
moved in any direction over the board through the medium 
of hinged arms, rigidly attached to the upper left hand corner 
of the drawing board. Straight edges having any of the 
standard scales upon them may be attached to the frame. 

There is also a Paragon Drafting Instrument accomplish- 
ing much the same purpose. It is attachable to a parallel 
ruler previously mentioned or it can be attached to a T sq. 
blade. The fixed center is the point of attachment and the 
ruling edges, two in number, can be swung around it at any 



Curves and Straight Lines Combined, and Sections 4r 

angle, replacing triangles and protractor, and also having 
variously scaled edges. 



20. Sectioning. 

It is not always possible to show all the facts of a subject 
by use of the elevation and plan heretofore spoken of, and 
even where possible, convenience frequently calls for a 
shorter way to attain the information. A cutting open of 
the subject, showing the interior is what is resorted to. This, 
is known as sectioning; the views of the cut portion are 
called sectioned views or simply sections. 

A section, in its simplest form then, means to cut any 
thing as with a saw and to show by some conventional or 
commonly understood means the plane of the cut and what 
lies beyond this plane when looking perpendicularly at it. 

The conventional or commonly understood means for 
showing the plane of the cut is to cover the parts cut through 
with evenly spaced parallel lines. They are not intended to 
represent or suggest a tinted surface, hence to distinguish it 
as a sectioned surface the hatching lines, as they are called, 
are ruled diagonally of the edges of rectangular forms. If 
the edges of a sectioned surface are vertical and horizontal, 
the most common condition to be met with, the sectioning is 
done generally with the 45° triangle resting on the T sq. 
Contiguous parts are sectioned lined in opposite directions. 
In any position whatever of the contour lines of the sectioned 
surface, the section lines are generally made at an angle of 
45° with them; for example, where the contour lines are at 
45° to the horizontal, the section lines may be horizontal or 
vertical. 



42 Notes on Practical Mechanical Drawing 

The weight of the Hnes used in sectioning should not 
exceed those of the outHne, they look rather better, generally, 
if made slightly lighter. Considerable judgment can be 
displayed in the adjustment of space and weight of section 
lines. Consulting practical drawings or the illustrations to 
this book will be helpful. The effect should never be coarse 
but pleasing, even, and not too obtrusive. 

Fig. 4 gives an example of sectioned surfaces. It can 
be seen that if nerrow spaces are sectioned by relatively 
widely spaced lines, the effect is coarse. If on the other 
hand, the spacing is too narrow the effect will be that of a 
dark tone obscuring the outlines and any errors in spacing 
are more noticeable. Again, the larger the surface to be 
sectioned the wider can be the spacing of the lines. Long 
narrow pieces should be sectioned by heavy lines closely 
spaced and large areas by light lines widely spaced. 

Draftsmen generally have a maximium and minimum of 
spacing of section lines that are not very far apart, nor do 
they use many different spacings because it is economical of 
effort if sectioning can be made more or less mechanical. 
One authority fittingly says : *" When a few lines have been 
done in section an unconscious rythmic action, as it were, is 
established, just as one beats time to slow or fast music 
without thinking, and the manipulation becomes mechanical. 
For this reason,' he goes on to say, 'a drawing to be inked 
should never be sectioned in pencil first, otherwise the result, 
is likely to be as bad as if one were to write his name with a 
pencil and then try to go over the lines with ink.' " 

Hence it can be seen that this rythmic action comes 
more readily when the eye is accustomed to a very few 
different sizes. 

* G. W. McCord, Mechanical Drawing?, P. 6. 



Curves and Straight Lines Combined, and Sections 43 




-44 



Notes on Practical Mechanical Drawing 



Where more than two surfaces are contiguous to one 
another it is customary to use 30° or 60° Hnes to distinguish 
the third surface, but these angles are not resorted to unless 
it is necessary. 

Sometimes contiguous surfaces, especially when large, 
are distinguished from one another by having the section 



rig. 


s. 




^P 


^ 


m. 


i 


1 







lines fall uniformly short of the limiting lines of the surface 
by a small distance, say V32 '^^ Vie of ^^ '\\\q^ as shown in 
Fig. 5. A section may be designated as a longitudinal or 
transverse section according to whether the plane of the sec- 
tion is parallel to the long axis of the subject or at right angles 
to it. 

If the plane of a section is horizontal, it is called a sec- 
tional plan, if vertical, a sectional elevation, or in other direc- 



Curves and Straight Lines Combined, and Sections 45 

tions it may be called simply a sectional detail. If a sectional 
plan, its place is above or below the elevation, according to 
the angle used in projection and it may take the place of a 
plan \\'hen it is not necessary to have the latter present. 
When it is, then the sectional plan may be placed either 
above or below the regular plan according to the angle of the 
projection, or if there is not convenient room for this, it may 
be placed to the right or left, orthogonally projected from the 
plan. Again, sometimes, according to circumstances, the 
section is placed independently of the regular projection 
views in any convenient place on the sheet. The importance 
of the section view and its value in giving data for construc- 
tion determine the latter mentioned choice of positions. 

Again, if the view is a sectional plan, a broken line, for 
which the convention is a variable, is drawn across the eleva- 
tion showing the position of the theoretical saw cut, and the 
ends of this line are lettered A — A or B — B, and so referred 
to in designating the sectional view (see Fig. 4). The broken 
line may consist simply of very heavy, short lines just enter- 
ing upon and on opposite sides of the elevation, to call atten- 
tion sharpty to the place. 

AVhile a section is theoretically a saw cut, subjects are 
not always continuously cut through. Only a portion may 
be sectioned or the plane of the section m.ay for convenience 
or economy of views, be in reality two or more parallel planes 
cutting through two or more parts of the subject; very 
rarely are the planes miade non-parallel, although such a 
condition is not prohibited by any written or unwritten laws. 
A ver}^ usual device is to represent a portion, say one half, of 
an elevation as in section. This, if the subject be symmetri- 
cal upon a center line, will save the drawing of one view. 



46 Notes on Practical Mechanical Drawing 

If the plane of a section moves from one place to another 
as just explained, some conventional line, usually that for 
center lines, is used to divide the planes or the sectioned from 
the non sectioned parts. The plane then terminated by this 
limiting line has no other limits. A solid limiting line is not 
used unless the material sectioned through actually ends at 
this place, and a new piece begins beyond it. 

Where different pieces are sectioned in a subject in the 
same sectional plane, considerable taste can be displayed in 
distinguishing parts one from another. Where the same 
piece reappears as cut through in the plane of the section it 
should be treated by section lines identical in weight and 
spacing so as to preserve, in other words, the continuity of 
material. 

Attempts have been made to standardize section lining 
by the adoption of certain weight and spacing of lines to be 
used as representing different materials, steel, wrought iron, 
cast iron, brass, etc. But, while a well known series has had 
wide publicity, that approved b}^ the A. S. M. E., and in 
use by the Government drafting offices, still its use is not at 
all universal. Each drafting office has its own way of treat- 
ing sectioning. Some use no conventions, others use a cer- 
tain few of the more important ones selected from the above 
mentioned series. 

There are insurmountable difficulties in the use of 
standard section lining which has prevented its universal 
adoption. It takes considerable extra tim^e, to render the 
conventions; it is also difficult, and next to impossible, to 
harmonize the efiects of an intelligent drawing, the proper 
distinguishing of sectioned parts with the conventions advo- 
cated, that is, materials cannot be made to stand out from 



Curves and Straight Lines Combined, and Sections 47 

one another in a desirable manner when the draftsman is 
confined invariably to a certain kind of line and spacing. 

However, a book on drawing which did not present for 
it? readers the standard conventions before mentioned would 



Fig. 8 



Cast /. 



Wr'ri. 



(5 tee/. 




Brace, 



Leac/^Babr, 










be considered very much out of place, therefore Fig. 8 is 
given for the benefit of those who wish to familiarize them- 
selves with them. 



48 Notes on Practical Mechanical Drawing 

The illustration shows a spacing and weight of line that 
are practical. Of course these are more or less governed by 
the area to be treated, varying with it. 

In the wrought iron the groups of lines should be sepa- 
rated from each other simply by a little wider space than are 
the lines of the group, the same of steel. 

The convention for glass is an attempt to illustrate the 
play of light one sees now and then upon looking into a room 
from the outside through a window; the several masses of 
tinting, which by the way should be expressed by lines more 
closely spaced than in sectioning, are irregular in their con- 
tour shape yet grouped together. The arrangement of this 
convention is after all a matter of the taste of the draftsman. 

Leather, sand, or packing material are expressed by 
about the same convention. It is made with the writing 
pen, touching the paper irregularly and spreading the nibs ; 
for packing the strokes may take the shape of irregular lines 
like short threads. 

In place of a conventional section lining, materials may 
be lettered W. I., C. I., S., etc., on the surfaces, to show what 
they are made of, or else a designating number may be used. 
The number may lie between limits which by arbitrary agree- 
ment stand for a certain material; for example, Nos. 1 to 
200 for cast iron, 200 to 300 for wrought iron, etc. 

A sectioned view should always show in full line that 
which lies within the plane of the section, all that is beyond 
this should also be shown in full line which is not covered by 
the surface sectioned. If it is desirable to show what is cov- 
ered it should be dotted as in any other hidden construction. 
Of course nothing should be shown of that part supposed to 
have been removed when the subject was cut through. 



Curves and Straight Lines Combined, and Sections 49 

Sectioned views are not used in working drawings unless 
it cannot be avoided or unless their use is economical of 
view^s, and consequently of time, and when not sacrificing 
clearness. They are used less as a vehicle for dimensions, 
also, than they are to show form, what is solid and what is 
hollo w^ what is continuous in the various materials. They 
are not desirable as a vehicle for dimensions because of the 
interference of the section lines with the dimension lines and 
figures. When dimensions have to be put across a dimen- 
sioned surface, space is left at least for the figures, sometimes 
for the dimension lines and the arrow heads. Aside from 
legibility, the presence of a dimension should be at once ap- 
parent through its prominence on the drawing. 

21. Some practical points about sectioning. 

Section lining should be done directly in that material 
in which the drawing is to be left, and the spacing calculated 
with the unaided eye. To do this well will require a little 
practice ; a few hints which follow may be found helpful. 

In the first place it is convenient in penciling, which is 
to be inked, to sketch the sectioned, surfaces roughly free- 
hand to show which are sectioned and which are not, and to 
show what direction of section lines to use. 

When possible hold an arm of the triangle, one edge of 
which is guiding the section lines, by the thumb and first or 
second fingers so that the triangle may be made to creep 
along as was suggested for the T sq. blade. Use the edge of 
the triangle only for an approximate adjustment of spacing, 
let the pen point give it more accurately. It will be noticed 
that with practice the pen can be tilted a little out of plumb 
and nearer to or farther from the ruling edge without sacrific- 
es) 



50 Notes ox Practical Mechanical Drawing 

ing quality of line, and that this little is sufficient to change 
the approximate adjustment of the ruling edge to the accur- 
ate place of the line to be drawn. It is very desirable to at- 
tain this proficiency and in this way. 

Mechanical devices called section liners have been in- 
vented for spacing lines evenly but they are not in general 
use by draftsmen. They fail in just the respect mentioned. 
The pen cannot be held so invariably the same way with 
respect to the ruling edge that the section liner can be de- 
pended upon entirely to space automatically. 

If a surface to be sectioned is broken up so that the lines 
in all places cannot be drawn continuously across it, as in a 
transverse section of a hollow cylinder, a line may be fol- 
lowed along from its beginning to its end across the subject 
before going on with the next one, or a group of lines may be 
treated in one place and afterwards in another on the oppo- 
site side. The latter is the method much to be preferred if 
certain precautions are followed, for it is exceedingly difficult 
to maintain an accurate holding of the pen "with respect to 
the ruling edge when the pen has to be lifted and lowered 
again in another place. If two opposing groups of lines are 
to be united farther along, each may be drawn readily and 
separately if one is stopped just short of uniting and the re- 
maining space, which should be sufficient to contain four or 
five lines, is calculated rather carefully by eye, and any in- 
accuracy in the alignment of the groups adjusted before they 
meet. This method requires less care and can probably be 
clone more rapidly than the first one mientioned. 

In the section view of features which wrap around one 
another like a valve with its stem, gland and body, it is de- 
sirable, if possible, in the penciling, to begin with the inner- 



Curves and Straight Lines Combined, and Sections 51 

most parts and develop outward from them because it will 
save erasure of parts which are covered up by those on the 
inner side. 

Sometimes labor is saved, in hurried work, by not sec- 
tion lining entirely across relatively large surfaces but by 
sectioning only around the edge, stopping the section lines 
along imaginary lines parallel to the edges successively of the 
surface to be sectioned. 

Sometimes forms are cut through which cannot be ac- 
curately represented by a surface hatched with lines. Such 
a form is the cross section of an I beam or a built up girder, 
the latter form being shown in Fig. 6. Such a thing as this 
is difficult because the surfaces cut through are so narrow 
that it is impossible to represent them to scale by a double 
line, in fact the ordinary line on a drawing might itself be far 
too heavy to represent this thickness. Scale in thickness of 
material then has to be sacrificed for effect in showing con- 
struction. Where it is possible, accurate scale should be 
adhered to. It is only in such subjects as the above where 
the error is apparent without explanation that the rule of 
accurate drawing should be broken. 

Long members of uniform cross section like I beams, 
etc., sometimes cannot be shown their true length in a draw- 
ing without reducing too much their transverse dimension. 
To overcome this they are assumed to be broken as shown 
in Fig. 7. The over-all dimension is given and, to save a 
separate view, the exact shape of the cross section may be 
shown on one of the pieces, as if the plane of the section were 
turned through an angle of 90°. 

As the rules of orthographic projectiori are violated in 
working drawings so, in sections, things are done which are 



52 Notes on Practical Mechanical Drawing 

not strictly projective or follow the theoretical saw cut. This 
is because clearness of construction is paramount. 

For example, it is of no use to section longitudinally 
through a bolt or nut, nothing is gained in clearness, in fact 
something is lost. The identity of the bolt or nut is not as 
readily distinguished. So, for this reason, it may be said 
that we never section longitudinally bolts, washers, shafts, 
rods, or other solid pieces having a relatively long axis pro- 
portional to their diameter. 

We do not, in sectioning a wheel with spokes, cut 
through a spoke longitudinally if it should happen to come 
within the plane of this section. The rim and hub are the 
important features, the spoke is but a relatively narrow 
connecting link between the two. If sectioned it is apt to 
give the impression of a wheel with a web or diaphragm 
connecting rim and hub. It does not make the forms clear. 
In this way, in other subjects, we arbitrarily skip over feat- 
ures which obviously come within the plane of the section. 

It may be set down, therefore, as a general rule that a 
rib, an arm of a pulley, or any comparatively thin piece 
should not be sectioned by a cutting plane which is parallel 
to its longest bounding surfaces. 

As a further illustration, when materials are sectioned 
through, the surface of the cut is not interrupted merely for 
the sake of showing a fastening or some other minor feature. 
For example, if sectioning longitudinally through a cylinder 
and its head, and if the bolts fastening body and head should, 
some of them, happen to come within the plane of the sec- 
tion, they would not be sectioned, but either omitted or shown 
in dotted where they passed through the sectioned material, 
and in full line elsewhere. 



Curves and Straight Lines Combined, and Sections 53 

On the other hand, if we have a sectioned side view of 
any thing having radially placed holes, and the plane of the 
section does not pass through one or more of them, nor is their 
arrangement clearly shown in another view, one hole should 
be cut through, and at its true radical distance from the cen- 
ter, to furnish information lacking elsewhere. 

A key-way in a collar should not be sectioned longitudi- 
nally with the collar, but should be shown with a dotted 
line. 

It is hardly worth while to multiply instances of viola- 
tion of projection in sections; new cases are likely to arise 
continuously. Suffice it that features are not shown in sec- 
tion where no information would be gained thereby, no 
matter whether they come within the plane of the saw^ cut 
or not. 

Sectional details are placed either near the part to 
which they are related or grouped together in any convenient 
place on the drawing, there is no rule governing. If placed 
near the principal form they are generally made projective 
with it, except that the sectional projection may be made 
on a supplementary plane not corresponding to the co-ordi- 
nate planes. Sometimes the section is revolved into a co- 
ordinate plane about a line as axis which designates, on the 
view, where the section is taken and it may be revolved from 
the actual position of the section or moved along the desig- 
nating line to a free place on the sheet. For example, the 
shape of the spoke of a wheel may be shown by a detail sec- 
tion on the spoke, limited by its limiting lines, or to one side 
on the line which shows where the section is made. See Fig. 
10. 



54 



Notes on Practical Mechanical Drawing 




Curves and Straight Lines Combined, and Sections 55 

22. Some practical points about and the care and hand- 
ling of drawing instruments. 

Drawings can be cleaned of the dirt which usually gets 
on them, with the soft pliable erasers, the needed rubber, 
the sponge rubber or stale bread crumbs rubbed over with a 
cloth, or with the hand, if it is not in too hot w^eather. But 
the readiness with which the cleaning can be done should 
not lead to carelessness in the penciling w^ork, for it makes 
unnecessary work, gives an unfavorable impression, as it 
should, to onlookers, and there is always the chance of injur- 
ing the lines somewhat by the cleaning process. The liquid 
drawing inks will stand very little erasure witli the pencil 
eraser without loss of blackness in the lines. To keep a 
drawing, in good shape, as the work progresses, cultivate 
early the habit of keeping the T sq. and triangles clean, using 
a piece of paper where possible over parts of the drawing 
not in immediate use, and, finally, keeping the hands off the 
work when they also are not in active service. 

A caution is here extended which will, if followed, aid 
in this respect. Cultivate the habit of standing erect at a 
drawing board, putting all the strain upon the back instead 
of saving it at the expense of the drawing board, giving an 
indolent appearance and endangering general physical 
comfort. 

Drawing instruments should be handled as little as 
possible consistent with necessary use. A fault is all too 
common, especially among beginners, of nursing instruments 
in the hand when not in use. Observe that the workman in 
any craft vv^ill always lay a tool down when he is done with 
it, even temporarily, and moreover, he lays it down where 
it is the least trouble to find it again. 



56 Notes on Practical Mechanical Drawing 

It is also equally desirable to be scrupulously careful to 
use the tools only for the purposes for which they were in- 
tended. Violations of this are to be found in using the T sq. 
as a hammer to put in tacks, the dividers as compasses to 
describe arcs, sticking the divider points into the board so 
the dividers will stand alone, etc., all of which tend to injure 
the tools. 

The tools should be at all times handy. With the T sq. 
always on the board, the triangles above it on the board and 
other tools in predetermined places from which they can be 
picked up without much, if any, hunting, and while the eyes 
are engaged on the drawing, will conduce to rapidit}^ and 
accuracy of work. Time is a very serious quantit}^ to be 
reckoned with in drawing. 

When finished with a drawing instrument for any ap- 
preciable length of time it is well to wipe it off with a cloth 
free of any moisture and dirt from the hand. A chamois 
skin is not the best thing for this purpose because it absorbs 
moisture freely from the atmosphere and gives it to the 
instruments, nor is it a good thing in which to wrap the 
instruments. Of course it is possible to prevent more or 
less discoloration of the German silver in instruments in the 
course of time but rust should never be expected or allowed 
to appear, for it indicates carelessness. 

Facility in the use of the ruling pen is eminently de- 
sirable as it leads to the proper use of the other tools, so a few 
more practical directions about it are in order. 

The proper holding of the pen has been minutely de- 
scribed. It remains to give more in detail the reasons for 
these directions. The pen is sharpened in approximately a 
parabolic curve, the legs are bowed, and when held perpen- 



Curves and Straight Lines Combined, and Sections 57 

dicularly to the paper the minimum of opening touches it. 
If tilted side wise a thicker Hne is apt to result, or if not 
noticeably thicker the way is open for a large amount of ink 
to flow out, and this is what happens when a very heavy 
line is described, sometimes completely emptying the pen 
and making a blot. Again, it is easier to see the place and 
length of the line to be drawn when the pen is held vertical. 

The greater care at all times should be exercised the 
thicker the line used or the fuller the pen is with ink. The 
beginner should carry less ink in the pen than after he be- 
comes expert. When occasion arises to use the pen for long 
lines or many close together, with the least interruption for 
refilling, a considerable amount of ink can be carried in the 
pen if the following directions are observed : Head the pen 
to start, the point very close to but not touching the paper; 
when ready, touch the pen to the starting point and instantly 
move on the line uniformly and .rapidly, the more rapidly the 
fuller the pen. .Stop and lift the pen in the same instantane- 
ous way. It is possible, in this way, to carry so much ink in 
the pen that if it is held stationary against the paper the ink 
would run all out at once. These same precautions hold 
w^hen making a very thick line with the pen ; the thicker the 
line the less ink can be carried. 

In drawing lines to go from or to a heavy ink line or 
border still greater care has to be observed that the border 
does not draw the ink out of the pen and cause a blot. The 
situation is illustrated in Fig. 10. It shows a series of lines 
close together where the edges of the lines are apt to break 
down and the lines run together. In cases of great danger, 
every other line or so may be begun late as shown in the 
figure and afterwards filled out when the ink dries. In 



58 Notes on Practical Mechanical Drawing 

patching these open spaces set the pen to make a finer line, 
matching only one edge of the line drawn, then by tilting 
the pen probably the requisite increase can be made if not 
with accuracy in one stroke, then in two or more ; a line can 



Fig. 10 





be added to easily but it cannot be reduced in size except 
by erasure first and then redrawing. 

A similar difficulty is presented in ruling a series of lines 
to meet or cross at a common point. Where possible it is 
best to draw the lines towards the meeting point, for there 
is less likelihood of the ink running out of the pen in lifting 
from than there is in lowering to the paper. 

If a pen fails to w^ork it may be due to several causes, 
(a). It may be set so tight that the ink cannot flow out be- 
tween the nibs. In this case it is better to open the pen 
liberally to a coarser line than desired and set it by trial 
towards the finer. It is found by experience that this saves 
time. 

• (b). The ink may have dried at the ends of the nibs, if 
not farther, and clogged the flow. The best thing to do is 
to at once clean and reflll. The use of a blotter or a piece of 
paper drawn through between the nibs is to be deprecated 
as only a poor substitute for poor conditions for working. 

(c). Owing to the presence of grease, or for other 
reasons, the ink, on first filling, does not run down to the 



Curves and Straight Lines Combined, and Sections 59 

point. Proper running may here be facilitated by opening 
the nibs a Httle and shaking gently, over a blotter or some- 
thing it will not injure if it blots, until the ink settles or drops 
out. If the latter, it may be found necessary to wipe the 
nibs free of overflow^ before using the pen to rule with. 

(e) . The pen point may be actually out of order, a little 
broken or one nib a little longer than another. This of 
course demands that they be sharpened ; but the pen should 
be tested for all of the other difficulties first. An injured pen 
will either not mark at all or it will make a ragged line ; the 
line, moreover, may be ragged on one or both edges. If the 
pen is merely uniformly dull, it will refuse to make a fine 
line, the line will simply fail entirely if the nibs are brought 
close together. 

A pen can he sharpened and tested in the following manner: 
A fine oil stone should be used for this, an Arkansas stone 
seems to be preferred. Bring -the nibs of the pen together 
as for drawing a very fine line, and hold for the rubbing at a 
small angle to the stone, 30° or less, and with the broad face 
of the nibs towards the stone. Rub to and fro in the direc- 
tion of the handle with at the same time a slight rocking of 
the pen in order to round the point. If too pointed it tends 
to cut into the paper and will not hold sharpness so long. 
To test for sharpness, drag it on a piece of paper as if making 
a line ; it ought not to scratch roughly or glide too freely, but 
bite slightly, that is, resist motion. If it seems to act as it 
should, clean thoroughly and then try with ink. Properly 
sharpened, the pen should make a very fine black hair-line 
\Aithout breaking and a broad line of sharp edges, even if 
the pen is tilted five or six degrees out of plumb in a plane 
perpendicular to the ruling edge. Try for a broad line first 



60 Notes on Practical Mechanical Drawing 

with this test in order to see if both blades are of equal 
length. If they are not, that side of the line at which the 
nibs are shortest will show ragged. If this test is successful 
and the line drawn is perfectly sharp and clear on its edges, 
test for fineness of line, by working from a wide line towards 
a narrow one. If it happens that the sharpening has pro- 
ceeded too far and the pen bites too deeply into the paper, 
or if one nib is slightly longer than the other, the pen may be 
dulled or the long nib be worn down by rubbing it on the 
stone with a rotary motion when the broad nibs of the pen 
are perpendicular to the plane of the stone. 

To determine the place of a line the ruling edge should 
furnish a rough approximation and the marking point the 
exact place as mentioned in Sec. 21. It is one of the impor- 
tant points in handling to be learned early. The nibs of a 
ruling pen, for example, being bowed will touch the paper 
slightly in advance of the ruling edge. If the pen is incor- 
rectly tilted until the nibs touch the paper at the ruling 
edge, a blot is almost sure to result, for the ink will touch 
the ruling edge. 

It may sometimes happen, when a number of lines have 
to be drawn which run in a variety of directions that waste 
of time is threatened in waiting for ink to dry. The ruling 
edge can be held slightly free of the paper and over the wet 
lines by using the thumb and first or second finger as a 
cushion underneath it or one ruling edge may be rested on 
and slightly overhanging another. In small work one tri- 
angle may be put with its open space over the lines to be 
drawn, and the other triangle rested upon it, crossing the 
gap. A method of inking will be shortly discussed which 
overcomes some difficulties of waiting for ink to dry. 



Curves and Straight Lines Combined, and Sections 61 

Errors in an ink drawing can be corrected so that the re- 
pairs are practically invisible. A knife will not do this 
unless used in conjunction with the ink eraser. In fact, 
cutting or scratching with a knife is so risky that it is safe to 
adopt the custom of never using it except under extreme 
circumstances. 

If an error occurs, take up as much ink as possible with 
a blotter, but do not use it under any ordinary circumstances 
to dry a line because it pales the ink. Then use the ink 
eraser, rubbing rather lightly and rapidly, not in one direc- 
tion or with one part of the eraser, but in all directions and 
changing the point of contact, because the rubber will heat 
and not work so well. Every vestige of the mistake should 
thus be removed, although it blurs a certain area around 
the error. Erasing shields are quite handy in restricting 
the area erased. A shield is a piece of sheet brass with vari- 
ous shaped holes in it. Next clean off all the sand by using 
the pencil eraser. If the surface of the paper is very much 
disturbed it may be necessary to burnish it with a piece of 
ivory or smooth metal. The difficult part of correcting 
errors now comes in putting back the ink lines. A line 
made upon an erased space is quite apt to spread a little and 
show larger than on the fresh paper, although the difference 
is very slight, therefore the pen should be set for a slightly 
finer line, and this added to by successive strokes. If in 
spite of all precautions, the place erased be treacherous, use 
two exceedingly fine lines as limits or walls, the di.stance 
apart of the thickness of the line to be drawn, and which, 
when dry, will prevent the filling ink from percolating into 
the rough paper. In case of a very wide line, the retaining^ 
walls may have to be built up gradually. In repairing also- 



62 Notes on Practical Mechanical Drawing 

it is necessary to overlap the correct part of the Hne suffi- 
ciently to include all that has been affected by the erasing. 
A ver}^ good hard drawing paper ought to permit several, 
say three or four, corrections over the same spot if skillfully 
managed. Corrections upon the rough side of tracing cloth 
are very easily made with the ink eraser and no burnishing 
is necessary. On the smooth side, however, erasing is diffi- 
cult and quite apt to irreparably injure the surface of the 
cloth. The greatest of care must be used by rubbing lightly 
to prevent trouble from this cause. A knife is almost sure 
to take off the surface, and if it does, burnishing will not 
repair the injury. 

A knife comes of service now and then in one of two 
w^ays, first to scratch off the crust of large blots or very w^ide 
lines, without attempting to remove the ink entirely, second 
to cut out an extremely small spot of ink or a slightl}^ over- 
lapping line. In the case of the latter, the knife should be 
run along the edge of the correct portion to cut it away 
sharply from the incorrect, then the error may be scratched 
free without leaving the correct line ragged. 

The scale is one of the indispensable tools of the drafts- 
man which has not yet been discussed. There are a number 
of kinds of scales made, divided broadly into fiat and tri- 
angular and again, into civil engineer's and architect's or 
mechanical engineer's. The civil engineer's scale is one in 
w^hich the divisions of inches are by even decimals, tenths, 
tw^entieths, thirtieths, etc. The flat scale may contain two, 
four or eight scales, according to the w'ay in which its edges 
are divided, and is a convenient tool because of its flatness. 
The triangular scales usually contain twelve different scales 
and, because of this wide range, are probably the favorites 



Curves and Straight Lines Combined, and Sections 63 

for all round general use. The civil engineer's decimated 
scale may be used in place of the mechanical engineer's scale 
by assigning certain values to the divisions v^^hich will be de- 
scribed shortly. A description of the mechanical engineer's 
triangular scale and its use will suffice for the fiat scales also. 

In engineering, when scale is mentioned, it generally 
means so many inches or a certain fraction of an inch to the 
foot, or so many inches or a fraction of an inch will stand for 
a foot of the actual thing drawn. To take a concrete case : 
On one face of the triangular scale, the edge is divided into 
3-inch major divisions, identified by numbers on the fiat 
surface, the edge is also divided into 1^ inch minor divisions, 
identified by numbers on the curved part of the scale. At 
the right a three inch space is divided into twelve major 
divisions to stand for inches and each of these again into 8ths. 
At the left a I-2- inch space is similarly divided, except that 
each space standing for one inch is divided into quarters. 
Hence by overlapping we have' two scales to an edge. To 
lay off a dimension the three inch scale we read the even 
feet to the left of the zero mark and the inches or fractions 
to the right. 

Certain points in the handling of the scale deserve to be 
carefully noted. It should be used as a scale, never as a 
rule, and the edge should be brought as close to the line to be 
scaled as it is possible to get it. With a sharp and round 
pointed pencil make a short straight stroke, not a dot, at the 
scale division and perpendicular to the edge, a length, say, 
of V32 of si^ inch. Transfer measurements with the scale 
itself, where possible, not with the dividers or compass, that 
is, indicate the size by scale measurement then set the com- 
pass to the marks made if it is necessary to strike an arc of 



64 Notes on Practical Mechanical Drawing 

that radius. It is a common fault and has been even advo- 
cated in hooks on drawing that the compass or dividers be 
set to size directly by holding to the scale edge. It is very 
undesirable in several ways and should be studiously 
avoided. 

It leads to economy of time, and certainly to greater 
accuracy, if the scale is used in place of the dividers. x\nd 
again, what is very important, where possible, successive 
measurements should be laid off with one setting of the scale, 
for in this way any error in one measurement will not be 
comtmunicated to all the others as it would if the scale w^ere 
reset after each measurement. 

The problems arising in the use of the architect's or 
mechanical engineer's scale group themselves under three 
heads. (1). To make a drawing a given fraction of the 
original in size. (2). Given the scale used to determine the 
fraction of size which the drawing is of the original. (3). 
Given the size of the space in which a drawing must be made 
to fit, to determine the scale to be used to get this reduction 
from the original. 

(1). To illustrate: Suppose it is desired to make a 
drawing one quarter the size of the original; ixl2 = 3; 
therefore 3 inches is the scale or size per foot to be used. 

(2). To illustrate: Suppose a drawing is made to a 
scale of one quarter of an inch to the foot, then, as J : 12 so 
the drawing is to the original or V48 "the size. 

(3). In solving this problem the fraction of size must 
first be determined by getting the ratio of the size of the 
drawing to the size of the original. This fraction of 12 inches 
will give the scale to be used. To illustrate: Suppose a 
subject 3 feet long is to be reduced in drawing to 1 J inches, 



Curves and Straight Lines Combined, and Sections 65 

the length being the determining dimension, then IJ: 
36x 12 = ^, or the scale is ^ inch to the foot. 

When problems do not come out as even as these, the 
nearest available scale is taken. 

A very common error arises from mixing up scale with 
fraction. A quarter scale drawing means a drawing made 
} inch to one foot, while a -J- size drawing means a drawing 
made 3 inches to a foot. In other w^ords when we speak of 
a fractional size w^e do not mean that fraction as the scale 
but that fraction of 12 inches, the foot being the unit. 

There is a special and popular form of scale made for 
mechanical engineering work which differs in divisions from 
the ordinary scale. The inch and not the foot is made the 
unit for subdivisions. The scales shown are for half size, 
quarter size and eighth size. The half size, for example, has 
a half inch divided again into halves, quarters and eighths, 
to represent those fractions respectively of an inch. 

It now and then happens that a purely arbitrary and 
exact scale is required, and has to be constructed. It can 
be readily done by a method based upon the geometrical 
principle that lines parallel to one side of a triangle divide 
the adjacent sides into proportional parts (see Fig. 11). 

The civil engineer 's or decimated scale is mainly a scale 
for use when the reduction is relatively large so that from 
10 to 100 feet will be represented by an inch, for it has di- 
visions of lOths, 20ths, 30ths, 40ths, and 50ths, of an inch. 
It can also be used in the same way as the mechanical en- 
gineer's scale. To illustrate: The twentieths scale can 
be used for J inch to the foot, five divisions being equivalent 
to one foot, two and one-half to 6 inches, etc. The thirtieths 
can be used for six inches to the foot, five divisions then 
^6) 



66 



Notes on Practical Mechanical Drawing 




Curves and Straight Lines Combined, and Sections 67 

equalling one inch. By thus assigning arbitrary values to 
the divisions, any ordinary mechanical engineer's require- 
ments can be fulfilled with the trouble only of interpolation 
for some of the smaller measurements. 

23. Exercise No. 13. Sectioning. 

]\Iake a sectional elevation complete of the cylinder 
head. Show the stuffing box gland as just about to enter 
the head. Show the one stud bolt in place beyond the plane 
of the section. Draw section lines a little over V32 o^ ^^ 
inch apart. 

Note: This may be done in pencil only or inked as 
directed. 

24. Exercise No. 14. Sectioning. 

(a). Make a longitudinal section of the outboard 
bearing for a heavy duty engine as shown, and through the 
center. Show a few principal dimensions only, overalls, 
diameters, distances between centers, etc. 

(b) . Make a longitudinal section of the outboard bearing 
for a heavy duty engine as shown, and through the bolt 
holes of the sole plate. Show a few principal dimensions 
only, overall, diameters, distances between centers, etc. 

Note : These two exercises may be done in pencil only 
or inked as may be directed. 

25. Exercise No. 15. Sectioning. 

Make a longitudinal section through the bench vise in 
the drawing room, taking it through the middle of the jaw. 
Show only a few of the principal dimensions. 



68 



Notes on Practical Mechanical Drawing 



^ 



G f 



iaaogf9-^. 



^ 



W 




Curves and Straight Lines Combined, and Sections 69 

Note: The same general type of vise is shown in the 
Scranton Correspondence series on mechanical drawing. 

This may be done in pencil only, or inked as directed. 

26. Exercise No. 16. Sectioning. 

Make a longitudinal section through the center of the 
expansion joint, an example of which is to be found in the 
drawing room. Show only a few of the principal dimensions, 
the diameters, lengths of the parts, &c. 

Note: This may be done in pencil only or inked as 
directed. 



70 Notes on Practical Mechanical Drawing 



; ■ CHAPTER III. 

IRREGULAR CURVES AND GEOMETRICAL 
DRAWING. 

27. Irregular curves. 

Irregular curves are those which cannot be drawn with 
the compass, they include the 2nd and 3rd degree curves and 
the higher plane curves. They must be plotted by points 
and then draw^n through these points ; the larger the number 
of points taken, the more accurate the data for the curve. 
But at least the drawing of them can only be approximate. 
Points should be plotted closer together in proportion to 
the sharpness of the curve or to its rate of change of curva- 
ture. The points are connected by use of a curved ruler. 
To use it requires considerable practice and knowledge of 
handling. 

If the hand and eye are true enough, the curve 
may be drawn most advantageously, after plotting points, 
first free-hand in pencil, then interpreted in ink. The 
value of free-hand treatment lies in the rapidity with which 
an accurate result may be obtained. The eye can be de- 
pended upon to detect small inaccuracies ; it is a most true 
instrument. To accomplish the free-hand treatment skill- 
fully, the same methods should be used as those in any other 
free-hand drawing. Since these may not be well in hand, a 
few words of direction will be given. 



Irregular Curves and Geometrical Drawing 71 

Swing the hand in the direction of the curve and through 
as many points as possible; when the motion seems to be 
true for recording the Hne, make a veryHght, fine and short 
stroke through each of the plotted points, giving a suggestion 
of the direction of the curve; next, if these records look 
right, put in similar short strokes between the plotted points, 
obtaining a still more complete suggestion. If the points 
plotted are fairly close, this suggestion ought to be complete 
enough to make refinement of the whole curve possible, 
erasing and truing here and there as needed until it satisfies 
the eye. When it does this it may be depended upon 
sufficiently to copy in ink. As before remarked, the eye 
can be depended upon to detect small inaccuracies better 
than the instruments. 

Of course the above directions are not necessary if the 
points are fairly close together and the draftsman has suffi- 
cient skill to handle the ink line directl}^ with the ruler. 

The correct shape for a curved ruler is of importance. 
There are many curves made that are of very little value, 
these are the ones which have the maximum of different 
curves included in the one tool. The curves of value are 
the ones which have the fewest and simplest curves in one 
tool. The best type probably for general all around use, is 
a curve w^hich is uniformly spiral in its characteristics, that 
is, goes from a relatively sharp curvature to a gradual one, 
possibly very near a straight line. The curve is applied to 
the points plotted with the direction of the change of curva- 
ture the same in both. It cannot be used successfully, for 
example, in a case where the curve to be drawn becomes 
more gradual towards the right, and that of the curved 



72 Notes on Practical Mechanical Drawing 

ruler, incorrectly placed, grows more gradual towards the 
left. Hence a curve ruler that has a double spiral, where the 
region of change from the one spiral to the other is concealed, 
will give trouble in matching. 

A rule having many different curves will be one scrolled 
out in the interior, and it is made of more or less fanciful 
shapes. But the curves in the interior are not valuable 
because of the difficulty of raising the rule from the wet line 
without blotting, for in order to remove either a curved or 
a straight ruler from a line drawn, it should be slid along 
free of the line first and then lifted. 

Any curved ruler can be used to make any curve; a 
straight edge can even be used to draw any curve by making 
a large enough number of adjustments, but the ideal con- 
dition is, of course, realized when the maximum of the curved 
ruler will match the curve. Frequency of adjustments in 
using the ordinary curve is no perceptible drawback to an 
experienced draftsman beyond the time consumed in mak- 
ing them, any more, in fact, than the effort involved in 
moving the T sq. up and down, or adjusting a straight edge 
to successive straight lines. 

It is not necessary for a draftsman to have many 
different curves in his kit. Constant familiarit}^ with a few 
curves will compensate for the time taken to adapt himself 
to one with which he is not familiar, but which more closely 
approximates the curve to be drawn. A thoroughly 
equipped drafting room, where there are many men working, 
is likely to be stocked with curves for specific purposes, like 
railroad curves, ship curves, ellipses, parabolas, etc., which- 
ever are frequently needed. 



Irregular Curves and Geometrical Drawing 73 

The drawn curve should be as unbroken as the theoreti- 
cal curve, and it is the execution of this which is difficult 
for the beginner. It involves two problems: (a) To 
match the curves ; (b) to conceal the successive segments of 
the line. 

To insure matching the curves, apply the rule to at 
least three points, more if possible, then draw, not as far as 
the ruler seems to match the curve, but a little short of it, 
the amount depending upon how rapidly the ruler departs 
from the curve to be drawn at the last discernable point. 
Again, in moving to the next segment, match the ruler to 
the part already drawn so that it corresponds with it for an 
appreciable distance back of the last point drawn to. 

To connect tlie segments of the line accurately, handle 
the pen as previously described for section lining, head the 
pen first to make a perfect alignment, then start to move on 
the line, or if drawing up to a line, and just before reaching 
it, tilt the pen, if necessary, to bring it into the ink line 
correctly, but do not overlap. It is handier, whenever pos- 
sible, to draw from, not to, a line, and in this case make the 
new line just touch the one already draw^n, not overlap it, as 
in so doing the wet line is apt to spread and show the 
joint. 

It is necessary, in using the pen with the curved ruler, 
to acquire an adjustable handling so that the blades of the 
pen are at all times tangent to the ruling edge; it involves 
holding loosely, so the pen can roll between the fingers. 
At the same time it is desirable not to work on the under 
side of the rule. Instead of this, either turn the drawing 
around or use a part of the ruler which will fit it and present 



74 Notes on Practical Mechanical Drawing 

an upper edge for lining. A form of pen, before mentioned, 
is made which adapts itself automatically to the ruling edge, 
known as a follower pen; it is swiveled into the handle. 

Economy of time can be effected by duplicating curves. 
If a curve is composed of units of similar parts, the rule may 
be marked on its surface with a pen or pencil, noting where 
the unit begins and stops, and some other reference point 
or two to aid in setting the ruler in place. This applies to 
symmetrical curves like the parabola, hyperbola and ellipse. 

In symmetrical curves, care should be observed to 
match with the ruler for an appreciable distance beyond 
the axis of symmetry, but also to draAV only to the axis. 

28. System in penciling and inking drawings. 

Successful work of any kind will proceed in a system- 
matic and orderly manner. The workman, through ex- 
perience, will adopt the shortest and most accurate ways, his 
most valuable qualifications being accuracy, neatness and 
speed. 

A system in penciling cannot be followed to advantage 
entirely, because the conditions in the development of a 
drawing vary quite a little, nevertheless, a general plan can 
be followed where circumstances permit. The following is 
given as such a system :* 

SYSTEM IN PENCILING. 

1. Draw border lines. 

2 . Draw match lines to guide in replacing the drawing 
if it is temporarily removed. 

* Cooledge & Freeman, Mechanical Drawing. 



Irregular Curves and Geometrical Drawing 75 

3. Block out space for title. 

4. Block out space for bill of materials, if any. 

5. Block out the views to be placed upon the sheet. 

6. Draw main center lines, and where these are to be 
inked, they may be drawn full light lines. 

7. Locate main lines of view^s. 

8. Draw small and inside lines. 

9. Put in dimensions and necessary notes. 

In inking a drawing there are two imperative conditions 
determining the most economical way of working: Firsts 
delays which are likely to occur in waiting for ink to dry; 
second, omissions likely to occur in things which should be 
lined in. Draftsmen are not uniform in their systems, but 
each one has that which to him seems to commend itself to 
avoid the difficulties above mentioned. There is, however, 
a general plan followed by all, and it is the purpose to discuss, 
this general plan in detail. 

The following is an order of inking which may be safely 
adopted and depended upon to fulfill all general require- 
ments : 

SYSTEM IN INKING. 

1. Ink all small circles and arcs of circles with the. 

bow pen. 

2. Ink larger circles and arcs with the compass. 

3. Ink irregular curves with the curved ruler. 

4. Ink all horizontal lines with the T sq. 

5. Ink all vertical lines with the triangle resting on 

the T sq. edge. 

6. Ink all 45°, 30° and 60° hnes in groups and in 

order. 



76 Notes on Practical Mechanical Drawing 

7. Ink other oblique lines not at the above angles, 

also in groups and in order. 

8. Do the section lining. 

9. Do the dimensioning. 

10. Do the surface tinting and shading. 

1 L Put in the lettering and descriptive matter. 

In large, complicated drawings it may be found quite 
an arduous task to put in any one of the first seven directions 
throughout a sheet of drawings, hence it may be well to 
treat a restricted area, one figure or a group of figures on the 
sheet, then the next group with the same treatment, and so 
on until the entire sheet is completed under one heading 
at a time. Under no circumstances should one figure, or 
part of a sheet, be completed in every detail before the rest 
of the sheet is carried through the same stages. This is a 
fault very apt to be indulged in by the beginner. 

Such a series of directions is exceedingly important to 
follow, and an unconscious adherence to them should be 
cultivated very early. That the importance may be more 
fully grasped, an explanation is here offered in detail of the 
main reasons for undertaking each stage in the order named. 

First, in general, it is well to do with a tool all that it is 
possible to do while having it in hand ; changing tools takes 
time, besides this, the eye and hand become increasingly 
adapt with use of a tool in performing a certain set opera- 
tion, and from minute to minute it is found there is percepti- 
ble change in facihty. Again, in working through one 
operation at a time there is more certainty that the entire 
subject will be uniformly treated, and no similar operation 
on any part of the drawing be omitted. 



Irregular Curves and Geometrical Drawing 77 

The bow pen, of course, is limited in range. In taking 
the small circles first, there is m^ore certainty of doing all 
that the bows will do than if the compass is used. And, of 
course, in general, the value of doing curves first at all, is 
that it is easier to make a straight line tangent to a curve 
than it is of drawing the curve tangent to the straight line. 
For a similar reason, the irregular curves are drawn after 
the compass curves, the latter are, in general, more in 
evidence, consequently more of them to hunt for on a draw- 
ing. 

Horizontal and vertical lines, as the enclosing lines of 
rectangular forms, also are most in evidence, and should be 
drawn among the first of the straight lines. It is well, if 
possible, to rule everything in the path of the T sq., as it is 
moved from the upper to the lower part of the sheet; but 
where a drawing is much broken up, it may be well to draw 
the long lines first, then the shorter, or else restrict the work 
to a certain area, or to one or more figures at a time, as before 
mentioned; or still further even, to divide the dotted and 
the center lines from the solid. Some authorities advocate 
the location of center lines the very first thing — it certainly 
has arguments in its favor. They are dependable land 
marks which control the correctness of everything else. But 
however the tool is handled in this respect, care should be 
taken to see that no lines it would make are omitted from 
the series ; they should be carefully checked before the next 
tool is taken in hand. For similar reasons the remaining 
straight lines are divided into groups. 

Section lining and dimensioning may conveniently 
change places in the series; they are given in the order 
named because the section lining concerns the construction. 



78 Notes on Practical Mechanical Drawing 

and theoretically, construction should be complete before 
any dimensions are put on. The advantage in making 
sectioning take second place, is that dimensions have somie- 
times to go across sectioned surfaces and determination of 
their place first, provides for their not being interfered with 
by the section lines. 

Dimensioning, itself, being one of the most important 
divisions of a working drawing, is profitably capable of sub- 
division because it provides against errors and omissions. 
Occasionally it is not practicable or necessary to include 
dimensioning as part of the penciling or preliminary opera- 
tions, so that both it and the inking of this stage go together. 
Hence, it may be considered a good plan to go over one figure 
at a time and record by arrow heads the radii or diameters, 
then the widths of everything needing specification, then 
the heights and the oblique dimensions. After these opera- 
tions are completed upon all the figures, or on the whole 
drawing, the values of the dimensions, whose place has been 
determined, can be put down with less risk, that neither the 
dimensions required or their value will be slighted. In 
inking the dimensions a similar plan should be followed 
with this addition, that, when the values are put on with the 
writing pen, the arrow heads at the terminals of a dimension 
line should be drawn first. The ommission of limiting 
arrow heads is a very common source of trouble in dimen- 
sioning, so that if the habit is formed of alwaA^s putting 
them in at first, one trouble will be overcome. 

Surface tinting and shading, v/hich are quite infrequent 
on working drawings, have reference only to pictorial or 
graphic interpretation, and should be performed separately 
as the very last of the operations. The tinting should 



Irregular Curves and Geometrical Drawing 79 

precede the shading because it and the section hning, while 
elastic in their character, yet together control the amount, or 
rather the intensity of the shading. To illustrate: A 
drawing ha^'ing much surface area broken up by tinting and 
sectioning will require a stronger treatment in the shading, 
that the latter may hold its place than it would were there 
little or none. It ma}^ be here remarked that there is much 
more possibility for pleasing effect and variety of treatment 
in a mechanical drawing than is generally supposed. A 
drawing looks well or it does not when the specific reasons 
are hard to assign; they may lie in this happy distribution 
of the masses of lines, somewhat as they do in a free-hand 
drawing. 

The lettering and directions for manufacture, which 
are listed last, it hardly seems worth while to make comment 
upon. Their place in the list is a rational one, it not being 
possible to place them elsewhere with any good reason to 
support the change. It is always likely, too, that at the 
last a need may be seen for some fuller explanation of 
construction. 

29. Geometrical drawing. 

Use all the mechanical aids that are available to get 
constructive results in a drawing, provided the processes do 
not involve too great an expenditure of time. For geomet- 
rical processes more frequently by their very multiplicity 
of steps, open the way for errors, and are practically more 
likely to result in faulty construction than if mechanical 
aids were used. But there are a few fundamental processes 
which every draftsman ought to know well, and there are 
some mechanical equivalents, also. As for the many 



80 Notes on Practical Mechanical Drawing 

geometrical constructions of a more or less simple forni, the 
student is recommended to consult the various hand books. 

Parallel lines are more easily obtained by mechanical 
methods. The T sq. and also the T sq. and triangles taken 
together, show the simplest cases. For others use either a 
straight edge and triangle, or two triangles. Place an edge 
of the triangle to the given line, and the straight edge or 
the other triangle against either of the other edges. The 
first triangle moved in either direction will present parallel 
sides. This is a common expedient for making a drawing 
when a T sq. is not handy. 

Perpendiculars and verticals mean two different things. 
Perpendicular is a relative term and means that one line is 
at 90° to the other, or normal, no matter what the direction 
of either line. Vertical, in a dra^\'ing, means a line which 
is perpendicular to a horizontal one only. In space it is a 
normal to a horizontal plane, or in other words, to the earth 's 
surface. This distinction should be borne in mind at all 
times, and neither the terms or the meaning mixed. 

Perpendiculars can be made most readily with the 
triangles and T sq. or straight edge. To draAv a perpendicu- 
lar to a given line, place the straight edge parallel to and at 
a short distance from the latter; for vertical perpendiculars 
this can be very easily done with the T scj. In the case of 
obhque lines, place one triangle against the given line and 
move it against the other triangle, as for parallel lines, until 
it is a short distance away, then use the second triangle 
against the first so that the perpendicular drawn can be 
made to intersect and cross the first, if necessary. 

It is a fault all too common to dra\v the perpendicular 
when the first triangle is in contact with the given fine. It 



Irregular Curves and Geometrical Drawing 81 

is not an accurate process, for in the first place it is difficult 
to set the triangle exactly to the point at which the per- 
pendicular is to be drawn, and in the second place it is not 
easy to dra^v the perpendicular down to the first line to 
touch it; with triangles in which the angles are at all worn, 
it is next to impossible. A facility in the use of the triangles 
for these processes is eminently desirable, for the latter one 
is almost continuously encountered. Sharp angles, where 
angles are constructed, is imperative in first class work. 

Right angles can be divided readily into halves and thirds 
by means of the 45° and 30° and 60° triangles, either with 
the assistance of a T sq., or without, by the process just 
described for perpendiculars and verticals. Hence a circle 
can be divided into four, eight, or twelve parts, and by 
bisecting one angle a new base can be obtained for halving 
all the angles and doubling the number of the above men- 
tioned divisions, for, put a straight edge parallel to this 
bisector and the triangle can be used as before. 

Similar triangles and equal angles may be constructed 
by the methods given for parallel lines ; although if the two 
equalities are far apart, geometrical process may be found 
preferable, namely, transfer of mxcasurement by compass. 

If a line to be drawn is longer than the edge of the 
triangle being used, the latter may be extended to continue 
the line by first moving its edge along parallel to the line, 
using the other triangle against the parallel edge. 

The lengths of the edges of the equal triangle should 
be transferred preferably by the scale rather than the 
compass, when possible, as it is more apt to be accurate. 
The use of the measurement a second time, that is to be 
transferred from the first triangle to the second, acts as a 
(7) 



82 Notes on Practical Mechanical Drawing 

check upon the size of the finst. Whenever processes are 
gone over twice a check is effected on the work. 

Tangency in geometry means identity of direction. Two 
curves are tangent to each other at a given point when they 
have the same direction at the point. The same direction 
also means that the common tangent to the curves is a 
normal to the radius of curvature of each at the point of 
tangenc}^ 

Since in geometry lines have no thickness, it follows 
that two lines in a drawing that are to be tangent to each 
other should be made not osculating lines, but identical, that 
is, the thickness of the lines at the point of tangency should 
be that of the thickest line only v/hich is used. Osculating 
means, of course, touching. If this included tangency, it 
would mean that where a number of curves were tangent 
at a common point, the thickness of the lines at the tangent 
point would assume very disagreeable, and perhaps, impos- 
sible proportions. 

To bisect any angle, as AOB, see Fig. 11. Lay off on its 
sides any equal distances Oa, Ob fro mi O as a center. Use 
a and b as centers for intersecting arcs having a common 
radius, but such, practically, that the arcs intersect normally. 
Connect the point of this intersection with O, and it will be 
the bisector. 

To draw a circle through three points, as a, b and c: Join 
the points by lines a — b and b — c; bisect these lines by 
perpendiculars, and the intersection of the latter will be 
the center of the desired circle. 

To divide a line into any number of equal parts, see Fig. 
11. From one extremity of the line OA, as O, draw a line 
OB making any angle with OA. With the scale, or dividers, 



Irregular Curves and Geometrical Drawing 83 

lay off any convenient unit from O on OB, as many times 
as parts into which it is desired to divide OA. Connect the 
last division with A, as 7 A. Then draw lines through the 
other divisions parallel to 7A; they will divide OA into parts 
proportional to those on OB. It is based upon the geomet- 
rical principle that parallels to one side of a triangle divide 
the remaining sides proportionally. In practice, this has a 



Fig 




6 



7y 



A 



5 A ^ 



A 

very ready application. To illustrate: If the distance 
between two parallel lines is to be divided into equal parts, 
in order that a number of parallels may be drawn to the first 
pair of lines, and they lie either horizontal or vertical, take 
the scale with any convenient unit, swing it so it touches 
both parallels with the number of parts enclosed between 
its limits, then locate these parts, and use the triangles, or 
T sq., to draw the parallels. It is a process very easily ac- 
complished. 

To draw a tangent to an irregular curve front a point 
without, see Fig. 12: Through T, the point of the desired 
tangent, draw" random secants through points on the curve 
as 1, 2, 3, 4, 5, etc. With T as a center, and any radius, 



84 Notes on Practical Mechanical Drawing 

describe an arc to cut the secants prolonged. On each 
secant lay off, from its intersection with the circle a distance 
equal to the chord length of the secant within the irregular 
curve, and measuring on the same side of the cricle as the 
secant with respect to the point T. Draw a curve through 




these points. Where this curve cuts the auxiliary circle, is 
a point in the tangent. For the tangent the chord length 
will be its minimum value. 

To inscribe a circle in any triangle: Bisect any two of 
the interior angles. The intersection of these bisecters will 
be the center, and its perpendicular distance from any side 
will be the radius of the required circle. 

To construct a regular polygon of any number of sides, the 
length of a side being given: Let AB, Fig. 13, be the length 
of a side, and let the potygon consist of x = 9 sides. With 
AB as a radius, describe a semicircle and divide it into nine 



Irregular Curves and Geometrical Drawing 



85 



equal parts by cut, and try methods v\4th the compass. Join 
B with X - 2, or division 7. Join B with 6, 5, 4, 3, etc., pro- 
longing the radii. AYith 7 as a center and radius AB, cut 



Fig. 13 




B - 6 prolonged at m, and join m with 7. Using m as a 

center and same radius, = BA, cut B - 5 prolonged in another 

vertex of the polygon, and so on. 

This solution is based upon the principle that if a 

1 • • 1 180(x - 2), 
regular polygon has x sides, each interior angle = 

and second, that the diagonals drawn from any vertex of a 
polygon make the same angles with each other as with the 
sides meeting at that vertex. 



86 Notes on Practical Mechanical Drawing 

To rectify an arc, in other words, to lay off on a straight 
Hne the length of a given circular arc (see Fig. 14). Let 
BA equal the given arc. Prolong AB to O, making 
OA = AB ^ 2. With radius OB draw an arc to cut a 
tangent to the curve at A in G. AC will be the required 



Fig. 14 



oy 




^-do 



length. This is an approximation, and useful only for short 
arcs. 

To draw an arc of given radius tangent to two given 
oblique lines (see Fig. 14) : Prolong the given lines to meet 
at 0. With O as a center, and the given radius, describe 
an arc AB. Parallels to the given hnes, and drawn tangent 
to the arc AB, will meet at C, from which perpendiculars to 
the given lines give the points of tangency, C being the center 
of the arc. 

Through a given point to draw a line to meet the inaccessi- 
ble intersection of two given lines (see Fig. 15) : Join A, the 
given point, with any points b and c on the respective lines. 
At any point on one of the given lines, as d, draw parallels 
to be and bA, and from where the parallels to be intersect 



Irregular Curves and Geometrical Drawing 



87 



the other Hne in c^ draw a parallel to cA. f, a vertex of the 
triangle formed, will be another point in the required line. 

30. The conies. 

The conic sections, or simply conies, as they are called, 
appear frequently in mechanics and machine construction. 
They are called conic sections, because they are the contour 
forms of plane sections of a cone of revolution. A cone of 

Fig. 15 




revolution is a cone formed by one line revolving about 
another, which it intersects, and with which it maintains a 
constant angle. 

If such a cone (see Fig. 16) is cut by a plane perpendic- 
ular to the fixed line, or axis, as a — a, the shape of the 
sectional plane will be a circle. If the cone is cut by a plane 
parallel to any position of the moving line, as b — b, the 
shape of the section will be a parabola. If the cone is cut by 
a plane making a less angle with the axis than that of the 
revolving line, as c — c, the shape of the section will be a 
hyperbola. In any other position, the cutting plane would 
give an ellipse in section. 



88 



Notes ox Practical Mechanical Drawing 



Ellipses, parabolas, and hyperbolas may be drawn in 
several different ways. A few of the more common and 



convenient will be given below ; 



Fig. 16 




31. To draw an ellipse by the focii method. 

To draw it by the principle, in other words, that the 
sum of the focal radii to any point on the c^lr^'e is a constant 
(see Fig. 17). The constant is equal to 2a. The focal radii 
are F P and FT, respectively. 

When the major and minor axis are given, the focii 
may^be obtained as follows: With a radius equal to the 



Irregular Curves and Geometrical Drawing 



89 



semi-major axis, and a center at either extremity of the 
minor axis, describe arcs to cut the major axis in points 
which will be the focii, for FY plus YF' = 2a. To find any 
point on the curve, as P, take any radius not less than XF 
or X'F^ and with center at F, describe an arc of a circle; 

Fig. 17 



XI 





V 




■1 \ 




V 


— 


-J 



with a radius equal to the difference between 2a, and the 
radius just taken, and a center at F', describe an arc to 
intersect the first one at P, which will be a point on the 
curve. There are three other points on the curve in addition 
to P which are symmetrical with respect to the axis, hence 
the practical method of procedure is to arbitrarily divide 
the major axis between the focus and the center of the 
ellipse into several parts, each to give two radii for four 
symmetrical points on the curve. With each radius taken 



90 



Notes on Practical Mechanical Drawing 



the four symmetrical points are obtained by striking arcs 
from both focii above and below the major axis. 

For careful drawing, more points will have to be plotted 
in the neighborhood of the major axis, than in that of the 
minor. It is w^ell to find a group of symmetrical points, as 
just described, complete, before proceeding with any con- 




struction for other points. Otherwise, there are apt to be 



errors m intersecting arcs. 



32. To construct an ellipse by the method of the trammel. 

The trammel is an instrument for mechanically con- 
structing an ellipse, not very successful practically, because 
of its lack of adaptability and its cumbersomeness, as well 
as large cost. It consists, fundamentally, of two tracks or 
guides at right angles to each other, and which constitute 
the major and minor axes. A third member, an arm, carries 



Irregular Curves and Geometrical Drawing 



91 



a marking point while two wheels, or lugs, fastened to it 
rigidly, move in the grooves in the first two members, and 
hence constrain the moving arm so that its marking point 
goes in the path of an ellipse. The operation can be more 



Fig. 19 




readily seen after a description of its practical equivalent 
(see Fig. 18). 

Take a piece of paper as a straight edge, and mark on 
it a point P. From P lay off a distance. Pa', equal to a, and 
also a distance, Pb', equal to b. Then with b' touching the 
major axis, and a' the minor axis, P will be a point upon the 



92 Notes on Practical Mechanical Drawing 

curve. To plot points then, move the straight edge around 
into as many positions as desired, and for each point plotted, 
indicate its place by a short stroke along the straight edge, 
and one perpendicular to it at P. This kind of stroke will 
identify the points most successfully. This method of 
plotting an ellipse is an excellent one, because of the 
ease with which the points can be located, and the ease, also, 
with which they can be placed where wanted. 

33. To draw an ellipse by the aid of the major and minor 
auxiliary circles. (See Fig. 19.) 
Draw the circles, as shown in the figure, upon the major 
and minor axis, respectively, as diameters. Draw any 
radius to cut the auxiliary circles in q and r, respectively. 
Through r draw a line parallel to the minor axis, and through 
q draw one parallel to the major axis. These lines will 
intersect in a point, P, on the curve. The points may be 
plotted, similarly, in all quadrants, or else in one and trans- 
ferred by measurement to the others. 

34 To draw an ellipse approximately with the compass. 

(See Fig. 20.) 

This is the method the mechanical draftsman will 
ahvays use, where possible, and it is a very good substitute. 
There are two ways, the following being the more common: 

Draw the minor auxiliary circle — it will cut the major 
axis in C. Connect B and A. Lay off on BA from B, 
the distance BC^ = AC. Next, bisect the line, C'A, 
and prolong the bisector, O 0^ to meet BO^ prolonged 
in 0^ 0' will be the center for an arc of a circle 
passing through B, which will approximate the ellipse. 



Irregular Curves and Geometrical Drawing 



93 



From the point in which this arc touches the bisector, O'O, 
draw an arc of another circle, passing through A, which has 
its center where the bisector cuts the major axis. To 
complete the curve, another center may be found on the 
other side of the major axis, and symmetrical with 0^ and 




one on the other side of the minor axis, symmetrical with 
the center C for the arc which goes through A. 

This is a method of drawing an ellipse, which, of course, 
more closely simulates the true curve, the nearer the ratio 
of the two axes is equal to one. But, in any case, it can 
easily be detected as composed of compass curves. 

The other method of approximation, seldom used, 
however, uses three centers for each quadrant, instead of 



94 



Notes on Practical Mechanical Drawing 



two, but it is more or less cumbersome, and if a closer ap- 
proximation than the above is desired, a cut and tr}^ process 
for the centers is economical of effort and time. 

If one has any facility in free-hand work, it is recom- 
mended that a quadrant be sketched in roughly, and then 





Fig. 2 1 

|_ P/ 


D 


/o f/ 1 


d' 


\|p 



copied as closely as possible with arcs, and using as many 
centers as needed for the purpose. The ellipse will not be as 
true as if plotted by points, but it will be a smooth curve and 
make a better general appearance than if constructed as first 
directed. In following this method remember that tangent 
circles, or regular curves have a common radius at the point 
of tangency. 



Irregular Curves and Geometrical Drawing 95 

35. To draw a parabola by means of the focus. 

First, a parabola is defined in mathematics, as the locus 
of a point which moves, so that its distance from a fixed 
point, called the focus, is equal to its distance from a fixed 
line, called the directrix. 

Let D D' (Fig. 21) be the directrix, and O F at right 
angles to it, the axis. Let F be the focus. Since the dis- 
tance of F from any point on the curve is equal to the dis- 
tance of that point from the directrix, to find any point 
on the curve as P, draiv a line parallel to D D' at any chosen 
distance from it. Then with this same distance as a radius, 
and F as a center, describe an arc to cut the parallel in the 
point, P. Two such points, P and P', will be found sym- 
metrical with the axis. One point must lie on the axis half 
way between the focus and directrix, namely, O, which is 
called the vertex. The entire curve is symmetrical on its 
axis. 

To plot a large number of points, for a good, smooth 
curve, divide the axis, arbitrarily, into a number of points 
starting at the vertex. Through these draw parallels to 
the directrix. Then with radii equal to these distances 
from the directrix, respectively, describe arcs from the focus 
as a center to cut the parallels in points. 

36, To draw a parabola by means of its envelope, (See 

Fig. 22.) 
If the approximate spread of the parabola as AB, 
together with the axis and approximate vertex, O, are 
known, the method is as follows: Prolong the axis and 
make the distance from O to C equal the distance from O to 
the line, AB. Divide the lines, AC and CB, into the same 



96 



Notes on Practical Mechanical Drawing 



number of equal parts, and connect them oppositely as 
shown. The parabola will be tangent to these lines, and if 
a considerable number are drawn, the parabola may be 



Fig. 22 




obtained with a fair degree of accuracy. The curve does 
not exactly go through the points, A and B, although very 
nearly. 

To find the point of tangency, of the curve with any 
one of the lines, say 1-1, lay off a distance on the axis, OE, 
equal to OD. At E erect a perpendicular to cut 1-1 in the 
point of tangency. 



Irregular Curves and Geometrical Drawing 97 

37, To draw a hyperbola by means of its focii. 

First, a hyperbola is defined in mathematics as the 
locus of a point which moves so that the ratio of its]distance 
from a fixed point called the focus, to its distance from a 

Fig. 23 




fixed line, called the directrix, is a constant and greater than 
unity (see Fig. 23). 

We shall work the problem, however, by the principle 
that the difference between the focal radii to any point on 
the curve is a constant. Let F F' be the focii, and O the 
center. Assume the vertices of the curve, A A^ at equal 
distances from O. A A' will also be the constant difference. 
(8) 



98 



Notes ox Practical Mechanical Drawing 



Take an}^ point on the axis a distance from F'' greater than 
F'A as F^Q, and with F^ as a center describe an arc; then, 
substracting the constant, A — A^ from F'Q, take the 



Fig. 24 




remainder as a radius, and F as a center, describe an arc 
to cut the first one in points of the curve above and below 
the axis. 

Now, for a simple illustration, consider that hyperbola, 
which is formed by a section of the cone parallel to the axis, 



Irregular Curves and Geometrical Drawing 99 

it can be easily seen that if these two elements of the surface 
(positions of the moving line) , which are parallel to the plane 
of the section, were projected on the plane of the section, the 
curve would approach, but never touch them. These two 
elements are known as the asymptotes of the curve. 

38. To draw a hyperbola, given the two asymptotes and 

any point on the curve. (See Fig. 24.) 
This depends upon the geometrical property of the 
hyperbola that the intercepts on any chord of the curve, 
between the curve and the asymptotes, are equal. 

Let AO and OB be the two asymptotes, and P the given 
point. Through P draw any chord, PE, lay off the distance, 
DE, equal to PE^ then D will be a point on the curve. By 
drawing any other chords through P or D and subsequent 
point found, as many points may be obtained as necessary 
with which to draw the curve. But while this is true, 
geometrically, it is not a very convenient method practically. 

39. To draw a hyperbola by the rectangle method. 

This is a method which is associated with certain prop- 
erties of steam, when its performance in an engine cylinder 
is plotted in a curve (see Fig. 25). 

Let AO and OB be two reference lines at right angles 
to each other, and let P be a point of the curve. Through 
P draw lines parallel to OA and OB, respectively ; also, draw 
any line, OQ. From the points in which the hne, OQ, cuts 
the parallels through P to OA and OB, respectively, erect 
perpendiculars, and these will intersect in a point on the 
curve, and so for as many points desired. 

LOFC 



100 



Notes on Practical Mechanical Drawing 



To find the point, O, given any two points, as K and L, 
on the curve and one of the reference Hnes : Draw a paral- 
lelogram upon K and L as vertices similar to tke one erected 
at P. A diagonal of the parallelogram will cut the given 

Fig. 2 5 




reference lines in the point, 0. The latter construction is 
in common use when applying the hyperbola to indicator 
cards of engines. 



40. The cycloid. 

The cycloids belong to a class of curves otherwise known 
as roulettes. A roulette is the path traced by a point upon 



Irregular Curves and Geometrical Drawing 101 

a curve which rolls upon another curve, the latter being 
fixed. The rolling curve is the generatrix, and that upon 
which it rolls is called the directrix. A cycloid may be 
described as a curve traced by a point upon a circle, which 
rolls on a straight line or another circle; although the 
cycloid, proper, is understood to be that curve traced by a 
point upon a circle Avhich rolls upon a straight line, and the 
distinguishing terms, epicycloid and hypocycloid, are used 
to mean the path of a point upon a circle which rolls upon 
the outside and the inside of another circle, respectively. 

The cycloidal curves are those used extensive^ for the 
outlines of gear teeth, and every draftsman should at least 
be familiar in the beginning with their construction. The 
aim in the construction of gear teeth is to get rolling contact. 

41. To construct the cycloid. (See Fig. 26.) 

Let AB be the fixed line upon which the circle, EDC, 
rolls. Suppose this circle to move in the direction of the 
arrow. When the circumrference has rolled a given fraction 
of its length upon the line, AB, the center, O', will have 
moved a linear distance equal to this, or to 0'^ that is, 
O' O'' = CP' = EP^ The point, P^ will lie on the directrix 
and the point, C, will have moved the distance towards the 
directrix that P' is from it originally. Hence draw a line 
parallel to the directrix through P', and with O'^ as a center 
and radius equal to the given circle, describe an arc to cut 
this parallel in the point, P, which will be a point of the 
curve. Repeat this process for as many points as desired. 
The curve is symmetrical upon the vertical line, EC. 
The tangent to the curve at C is parallel to the directrix. The 



102 Notes on Practical Mechanical Drawing 





Irregular Curves and Geometrical Drawing 103 

tangent at A is perpendicular to the directrix. If the circle 
continued to roll on AB it would generate another loop, and 
the point, A, would be a cusp of the curve. In gear design, 
only a small portion of the curve, in the neighborhood of A 
or B, would be used for the line of the tooth. 

42. To draw the epicycloid. (See Fig. 26.) 

The epicycloid, and also the hypocycloid, are the more 
common curves for gear teeth ; the cycloid is limited to the 
teeth on a rack. The directrix is a circle, i\OB, whose 
center is at F. When the circle, ODC, has rolled through a 
given circumferential length upon the directrix, O — C^ the 
center will have traveled a greater distance, proportional to 
its distance from the center, F, or O' — 0'^ Assume the 
circumferential length to be one-twelfth, the point, P'' will 
have come down to the directrix, and C will have come 
nearer the center, F, by as much as P'' moved toward it, or to 
the position of P'. Hence through P' draw the arc of a circle 
with center at F, and an arc of the generating circle from 
C as a center. Where the two arcs cross, will be a point 
of the curve of the epicycloid. 

The curve is symmetrical upon the line, F — O. The 
tangent to the curve at C is normal to the radius, FOC, and 
the tangent at A is normal to the directrix, or equal to the 
radius, FA. 



43. To draw the hypocycloid. (See Fig. 26.) 

The hypocycloid is similarly constructed to the epi- 
cycloid, the generatrix, or rolling circle, moving on the inside 
of the directrix. The epicycloid is the curve of the face, or 



104 Notes on Practical Mechanical Drawing 

upper half; the hypocycloid, the flank or lower half of the 
tooth outline. The center of the generating circle, it will 
be seen, travels through a shorter linear distance than the 
points on the circumference.. When the circumference has 
rolled off a distance, O — 0^^^ the center will have traveled 
to O^ ; the point, D, will have moved a distance farther 
from the center, F, equal to the distance of P^'' from the 
directrix. Hence with O^ as a center, strike an arc of the 
generating circle, and also draw an arc of a circle thsfugh 
PI, whose center is at F. Where these two circles intersect 
will be a point of the curve. If the circumference of the 
generating circle will go an even number of times into that 
of the directrix, there will be that even number of loops, or 
cusps. If the generatrix does not go an even number of 
times into the directrix, then the cusps will not close entirely. 
Both epicycloid and hypocycloid have a common tan- 
gent at the points, A and B, which tangent is a radius of the 
directrix. 

44. Geometrical definitions, terms, etc. 

Curves, in a mathemiatical sense, include straight lines 
ell as curves. A straig^ht line is a curve of infinite radius. 



as w 



■^fe 



A plane figure is a plane bounded on all sides by lines. 
If the lines are straight, the space which they contain is 
called a rectilinear figure, or polygon, and the sum of the 
bounding lines is the perimeter of the polygon. 

Polygons are named according to the number of their 
sides as a triangle, quadrilateral, pentagon, hexagon; a 
heptagon, of seven sides; octagon, of eight; nonagon, or 
enneagon, of nine; decagon, of ten; undecagon, of eleven; 



Irregular Curves and Geometrical Drawing 105 

dodecagon, of twelve. Polygons are supposed to be regular 
unless otherwise stated. 

A diameter of a polygon is any line drawn through the 
center of a figure, and terminated by the opposite bound- 
aries. 

The long diameter of a polygon is the diameter of its 
circumscribed circle. This is also called a diagonal. 

The short diameter of a polygon is the diameter of its 
inscribed circle. 

A polyhedron is a solid bounded entirely by planes. 

There are only five regular polyhedrons, viz. : 

The tetrahedron, bounded by four equilateral triangles. 

The hexahedron, or cube, bounded by six equal squares. 

The octahedron, bounded by eight equilateral triangles. 

The dodecahedron, bounded by twelve equal pentagons. 

The icosahedron, bounded by twenty equal equilateral 
triangles. 

A prism, is a polyhedron having two of its faces, called 
its ends or bases, parallel, and the rest parallelograms. 

A par allelo piped is a prism whose bases are parallelo- 
grams. 

The axis of a prism is a straight line joining the centers 
of its ends. 

The axis of a pyramid is the straight line from its vertex 
to the center of its base. 

A right prism, or pyramid, has its axis at right angles to 
its base. 



106 Notes on Practical Mechanical Drawing 



CHAPTER IV. 

WORKING DRAWINGS. 

45. The difference between 1st angle and 3rd angle pro- 
jection. 

By angle of projection is meant that diehedral angle 
between the two co-ordinate planes of projection in which 
an object is placed. For working drawings the choice, only, 
is open of either the first angle, or the third angle, for in 
either the second or the fourth, the plan is quite likely to fall 
behind or in front of the elevation. If the distances of the 
elevation and plan from the ground line are made to differ 
by a sufficient amount, this super-position can be avoided, 
but an equal difficulty is encountered in not being able to 
distinguish which is second angle, and Avhich is fourth angle, 
for the relation of plan to elevation does not, of course, 
determine it. 

Now, in the first angle projection, be it observed, that 
the object is projected upon the vertical plane from a center 
of projection, which may be assumed to be on the same side 
of the plane as the object. This is also true of the horizontal 
projection. To be consistent, an end view of the object 
should be that obtained by projecting it from a center on 

the same side of the plane as the object. For illustration: 
The view of the left hand end of an object would be placed 
on that plane which was to the right of the object, and the 
view of the right hand end would be projected upon the 



Working Drawings 107 

plane at the left. Now, if the same center is used, and an 
object be drawn in vertical projection in the third angle, it 
will be projected through the vertical plane, for the center 
is on the opposite side of the plane from the object. There- 
fore, to be consistent, the end view should be obtained by 
use of a center, which is upon the opposite side of the plane 
from the object. We see that if this is done, the view of the 
left hand end of an object will lie at the left, and that of the 
right hand end at the right. 

It is manifestly convenient to have this latter condition 
of affairs in a working drawing, because it conduces to 
legibility, and (in fact) it has been quite universally adopted. 
Care should be taken by the beginner not to be thoughtless 
in the use of either angle at pleasure, and in not mixing the 
two up in a drawing. 

Figures 27 and 28 show the first and third angle pro- 
jection, respectively. 

46. The helical curve and the screw thread. 

The ordinary V and square thread screws are based 
upon a curve known as the helix ; we will note something of 
the properties of the curve first. 

If a point moves around the surface of a cylinder at a 
uniform rate, and at the same time moves at a uniform rate 
in the direction of the axis of the cylinder, it will generate 
the helix. It can be seen from co-ordinate geometry that a 
curve plotted between co-ordinates, which have a directly 
proportional relation to one another, will be a straight line. 
The helix is such a curve, and it may be defined as the short- 
est line which can be drawn upon a cylinder between two- 



Fig. 27 




Fig. 2 




<.-«-^* 




r .^-^ 




> 



110 Notes on Practical Mechanical Drawing 

points that lie neither upon the same right section, or upon 
the same right line element. 

To study the curve in projection, draw a cylinder in the 
first angle (as Fig. 29) with axis parallel to the vertical plane. 
Assume a point to be at o, and to move around the cylinder 
in the direction of the arrow through equal distances, 1,2, 
3, etc. Let it move also up the cylinder through any given 
distance, until, after it has completed one revolution of the 
cylinder, it reaches a position, P', directly above o'. The 
distance, oT^ is known as the pitch of the curve. Now, as 
both motions are uniform, the point will travel to 1 , which 
is one-twelfth of the circumferential distance in the same 
time that it travels one-twelfth of the distance of o'P' towards 
P', and to 2, which is one-sixth of the circumierential length 
as it goes one-sixth of the distance, oT', towards P^ and so 
on. Hence to plot the curve, divide the circumference of 
the plan into any convenient number of equal parts, and 
the pitch into the same number of equal parts. By noting 
the points of intersection of the perpendiculars to the ground 
line, through the divisions of the circumference and parallels 
to the ground line, through the corresponding divisions of 
the pitch, points of the curve may be found. 

Certain peculiarities of the curve deserve notice : (1 ) It 
is tangent to the contour elements of the cylinder at points, 
o' and 6. (2) It changes curvature at point, 3, midway of 
the contour elements. The tangent to the curve at 3 shows 
the angular pitch, which is the ratio of the linear pitch to the 
circumferential distance. (3) The curve is sharpest at 
o', and gradually grows straighter until at 3 it reaches a 
straight line for a very short distance. (4) It is symmetrical 



Working Drawings 



111 



in parts with respect to the axis of the cyhncler, and to Knes 
perpendicular to the axis, so that the curve from o' to 3 is 
a unit which is repeated throughout the path of the point- 



Fig. 2 9 




112 Notes on Practical Mechanical Drawing 

If the pitch is lessened, the curve at the contour ele- 
ments of the cylinder grows sharper, and at the middle of 
the cylinder straighter, approaching throughout straight 
lines oblique to the axis of the cylinder. When in the 
ordinary screw the pitch is exceedingly small, relative to the 
diameter of the screw, it is next to impossible to draw the 
curve correctly. The pitch in the screw means the number 
of threads per inch of length, or the number of coils of the 
curve per inch of length. 

In the V threaded screw three curves are shown, one 
theoretically w^ound around a larger cylinder at the crown 
of the thread, and two wound around a smaller cylinder, at 
the base, or root, of the thread. In the square threaded 
screw are shown four curves, two at the croAvn and two at 
the root. The appearance of these two threads is shown 
in Figs. 30 and 31. 

It is to be particularly observed that the contour lines 
of the V thread do not meet at the crown of the thread in 
sharp angles, but each is tangent to the curve of the crown. 
Again, these lines do not meet at a point which lies on the 
cylinder upon which the root curve is theoretically wound, 
but they are tangent to the root curve, and cross one another 
a little outside of it. These facts are neglected in any prac- 
tical drawing of the thread, but should be com.prehended. 
They are, unfortunately, too often incorrectly shown in 
careful drawings of the thread in well known text books. 

The diameter of a screw, as dimensioned, always stands 
for the diameter of the croAvn line of the thread ; this does 
not indicate the strength of the screw. The strength is 
determined by the diameter of the root curve of the thread, 



Working Drawings 



113 




Fig. 3 1 




Working Drawings 



115 



being the minimum cross section of the material of which 
the screw is made. 

Unless, in exceeding^ rare cases, a large screw is to be 
drawn to show up especially well, a conventional method 
of showing the thread takes the place of the accurate one. 



Fig. 32 





^7^ 



i! i 
II I 



The first change from the accurate thread is to make the 
curves straight (as shown in Fig. 32). The next change 
to make is, in the case of the V thread, to omit the saw tooth 
edge, leaving just the longer and shorter lines, as .shown, 
making the limits of the screw a cylinder. Another conven- 
tion is shown also in the figure, one which suggests, in a way, 
roundness with a sacrifice of the screw^ characteristic. Square 
threaded screws are relatively rare, and there is no particular 
convention in use to represent them beyond making one 
thread of full lines and dotted limiting lines for the others 
as shown. Sometimes this is even done in the V thread. 



116 Notes on Practical Mechanical Drawing 

It will be observed that the Hnes of the thread have a 
sHght incHnation upAvard toward the right; the direction 
of the slant of the lines, in all positions of the screw, can be 
ascertained in this w^ay by looking in the direction of the 
axis of the screw. For left handed threads, which are rare, 
the slant is upwards tow^ard the left. The tap for a screw 
(see Fig. 31), if shown in section, will have its lines the 
reverse of those in the screw, because it is the duplicate of 
the curves on the rear half of the screw, which in the latter 
are not seen. 

In ordinary drawing, of course the pitch, as conven- 
tionally treated in Fig. 32, is not measured but estimated. 

The Whiteworth standard has an angle of 55° between 
the sides of the thread. The crown and root of the thread 
are both rounded off. The amount taken from the crown, 
and that added to the root of the thread, being equal to 
one-sixth of the total depth of the thread. Let D' -- diam- 
eter at the bottom of the thread, D = outside diamxCter of 
the thread, and N = number of threads per inch; then 

D = D'-lf^^seeFig.33). 

The U.S. standard proportions, devised by Mr. William 

Sellers of Philadelphia, has an angle of 60° between the 

sides of the thread. The crown and root are cut off fiat ; the 

amount added at the root being equal to that taken from 

the crown; the depth of the flattened face being equal to 

one-eighth of the depth of the thread. Using the notation 

1.299. 
as given above, D = D' — — 

There are other forms of thread occasionally used 
besides the V and square thread. The buttress thread, for 



Working Drawings 117 

example, is shown in Fig. 33. It is used where the screw is 
a transmitter of power in one direction, or where it is used 
to resist force in one direction. It may here be noted that 
a screw to transmit motion may have a large or steep pitch 
in proportion to the speed of the screw. If the speed is 
rather great, and yet it is desired to keep the screw strong, or 

Fig. 33 







t--p-*i 



KKri_nIh 



^ 



even for the latter reason alone, it may have a double thread 
or a triple thread. Thus, for one revolution of the screw it 
will travel axially two times the pitch, or three times the 
pitch, etc. An illustration of a screw with steep pitch, to 
give relatively large axial motion, is shown in the thread 
on the spindle of some valves. There is even a certain point 
which can be reached in the pitch of a screw thread, that 
longitudinal pressure of the screw Avill turn it. This is 
illustrated in the self-acting screw drivers. 

A truncated V thread is one in w^hich the crown and 
root have "been very materially flattened. It is a kind used 



118 Notes on Practical Mechanical Drawing 

in the spindles of some valves, as before mentioned. A form 
of truncated V thread, known as the Powell thread, is shown 
in Fig. 33. 

47. The drawing of hexagonal and square-headed bolts. 

Bolt heads and nuts are almost universally made of the 
hexagonal, or the square form, so as to be convenient to 
grip with a wrench. The hexagonal form is preferable, 
because in cramped places the hold of the wrench can be 
changed after turning through an angle of 60° (see Fig. 34). 

The sizes of the heads, both hexagonal and square, are 
universally standard for those in common use. Bolts are 
either cast, cut, or drop forged. The sizes are determined 
as follows: Let d = the diameter of the bolt, D the diame- 
ter of the head, then the formula is D = lid+ J'^ D is the 
true diameter of the hexagonal and square forms, namely, 
the perpendicular distance between the middle of opposite 
faces. It is taken this way so that the wrench for either 
will be the same, and so that the quantity may be readily set 
off with the scale. The diagonal of a hexagon is an awkward 
quantity to figu.re out, involving, as it does, a decimal; it 
is an incommensurable quantity compared with the di- 
ameter. 

The heads are not left in the prismatic form, exactly, but 
are chamifered. The underside of the head is left fiat. In 
nuts, both hexagonal faces are sometimes chamfered. A 
nut that is to tighten down on a fiat surface will work better 
into place without cutting the material, if its corners are 
rounded. To get the chamfer, the bolt is put in the lathe, 
and the cutting tool set at 30° to the axis of the bolt, and the 
head cut until all the edges are removed. The surface of 



Working Drawings 



119 



the cut is a cone; the intersection of the plane surfaces of 
the head with this cone give hyperbolas, very short arcs, 




Fig. 34 



"""^p^ 



' y \^ 



^ 



¥ 





however, differing so slightly from the circular that never in 
practice w^ould any draftsman render them accurately, no 

In finished bolt heads, the 



matter how exacting the work. 



120 Notes on Practical Mechanical Drawing 

dimensions are somewhat less than the formula given, being 
D = 1 Jd + Vie''- The height of a bolt head is approximately 
equal to the diameter of the bolt, in fact, it is different for 
different diameters. 

There is a generally universal method of drawing the 
chamfer (shown in Fig. 34). The center for the middle 
face is taken such that the arc, whose radius is equal to d, 
shall fall just a little short of the top line of the head. The 
radius for the smaller arcs is taken by cut and try methods, 
such that the arcs will be level with the larger arc, and cut 
the larger at its intersection with the edges of the middle 
face. 

In less careful drawings, the curve of the chamfer is 
made tangent to the upper edge of the head, and the bevel 
at the right and left may or may not be omitted. In still 
more hasty work, the angles are just slightly rounded, as 
shown at the right in the figure — this being done with the 
writing pen. Or, in still smaller work, the chamfer may be 
omitted. 

In working drawings bolt heads and nuts are always 
shown in the same positions. The elevation of a square 
headed bolt will show the one rectangular face. The eleva- 
tion of a hexagonal bolt will show either two or three faces 
symmetrically placed with respect to the axis of the bolt. If 
one view only of the bolt is shown, it will be that of three 
faces, the point being that the showing of three faces identi- 
fies the bolt as hexagonal, and of one face as the square. It 
is not uncommon in large m.achinery to see bolts of a size 
all set the same, that is, their rectangular faces parallel. 

Bolts are made with heads shaped differently from the 
hexagonal and the sc[uare. One form is a cylinder with the 



Working Drawings 121 

sharp edges of the upper base of the cyhnder rounded off. 
The diameter of the head varies from 1 .3d to 1 .4d. A spheri- 
cal head is also used, really not a sphere or even a hemi- 
sphere, but only a segment of diameter about 1.5d, and 
height, .75d. 

Machine screw is a term used to cover all threaded 
members to screw in metal as distinguished from wood. In 
a narrower sense, it is used to designate those screws which 
go by numbers, varying usually by thousanths. The threads 
are similar to the bolts proper. The fillister head (another 
name for the cyHndrical) is, as shown at the left of the 
middle row of Fig. 34, a combination of the cylindrical 
and spherical. The flat head is, as shown at the middle, 
and the button head, otherwise the spherical shaped head, 
before mentioned, is shown at the right. These same 
shapes are used for bolts, also, except that the groove for 
the screw driver is left out. 

There are varieties of bolts named according to the 
function they performx! The tap bolt, used to fasten two 
pieces together, running free through one piece and screwing 
into the second ; a stud or stud bolt, a bolt having no head 
but tapped into a piece, the free end being threaded to 
receive a nut. It may be used as a point of attachment, or 
center of motion. A set screw is a screw or bolt which 
presses on a piece so as to prevent the rotation or sliding of 
that piece, as the screw which holds a small pulley to its 
shaft. 

The strength of a bolt depends upon the diameter at 
the root of the thread as well as upon other things. Some- 
times the shank of a bolt is made less than the outside 
diameter of the threaded portion, making of it a stronger 



122 Notes on Practical Mechanical Drawing 

bolt, for reasons of machine design, not the province of this 
work. It is sometimes erroneously called a bolt of uniform 
strength. Usually, a part of the shank is left of the diameter 
of the threads, so as to prevent play of the bolt when in place 
(see Fig. 34). 

In ordinary machine bolts when threaded up to the 
head sometimes a groove is cut next to the head, as shown 
at the lower right in Fig. 34. It is impossible to cut a thread 
with a lathe up to the head, so the groove is put in as a 
finish. 

In machinery where a bolt is to go into a piece that is 
not otherwise smooth finished, frequently a small surface 
is raised to receive the pressure of the head, called a boss. It 
is left, in the case of a casting, of sufficient height that it can 
be cut down with the shaper or planer to a smooth surface. 

When a machine bolt, together with its nut, is shown 
in place in a drawing, to distinguish the square or hexagonal 
head, from the square or hexagonal nut, the bolt is shown 
as extending for a short distance, say IJ threads beyond 
the nut. 

vSometimes bolts have a square shank just at the head 
to sink into a square hole to keep them from turning. This 
is conventionally represented as in Fig. 35. The same con- 
vention is used for that portion of a shaft which sets in a 
bearing. 

Rivets for permanently fastening two or more thin 
members together are really short bolts with permanent 
heads on both ends. The heads of rivets are conical, 
spherical, cup shaped or pan headed, as shown in Fig. 35. 
The conical shape is the most common obtained by the use 
of the ordinary hand-hammer. If the cup head or pan head 



Working Drawings 



123 



is desired a different tool has to be used at the last in finish- 
ing, known as a 'snap,' or die, and a heavy hammer. A 
modified form of conical head is shown on the second row 



Fig. 3 5 




at the left. The approximate proportions are shown by 
dimensions on the figures given in terms of d. 

The exact interpretation of the dimensions shown is 
not important in ordinary drawing. The diameter of a bolt 
or rivet being laid out, the adjuncts can generally be treated 
with sufficient precision by eye for ordinary use. 



124 Notes on Practical Mechanical Drawing 

48. Orthographic projection and working drawing. 

Orthographic projection is the language in which work- 
ing drawings are written, but a dimensioned orthographic 
projection of anything does not necessarily constitute a 
working drawing of that thing. . 

A working drawing must be simple and plain in its 
features, easy to be interpreted, yet explicit. While pro- 
jection calls for a certain set of views to complete the defini- 
tion of form, the working drawing does not, for if one view 
of a piece Vv411 suffice to tell a workman how to make it, only 
the one view need be made. On the other hand, however, 
more views may be required in the working drawing than 
are required in orthographic projection, for sometimes 
assembly views are needed to show relation of all parts and 
detail drawings of each component part in addition. Third 
angle projection tends to legibility, and is the most usual 
medium for showing working drawings; it brings the front 
and end views into intimate relation to one another. The 
principles of orthographic projection are frequently violated 
in working drawings wherever modification will aid in legi- 
bility^ or economy of time in drawing. This was pointed out 
in discussing sections, and it will be again further treated a 
little later. 

There is no way to formulate this difference between 
the two under rules for there are no fixed ones. Each case 
has to be treated by itself when the occasion arises. Judg- 
ment and knowledge gained through experience are the only 
rehable aids. The draftsman should, as far as possible, place 
himself in the position, in imagination, of the one who is 
going to construct from his drawings, and in that way arrive 
at a conclusion as to what would be desirable in the wav of 



Working Drawings 125 

views. Unless the draftsman does this, he is apt to make 
his drawings too brief, to economize time and effort at the 
expense of the workmian 's time. From the w^orkman 's 
standpoint, many tim.es, drawings are not explanatory 
enough; he will w^ant them too elaborated wdth directions. 
A mean of these two has to be struck. For example, ^^'here 
hidden forms can be expressed by dotted lines, without 
hampering the workman in his requirements, the draftsman 
is privileged to use it to simplify his work. 

49. Of what a set of working drawings is composed. 

If a working drawing is required of a group of mechan- 
isms or subjects somew^hat widely separated, a diagram 
drawing m.ay first be made to determine upon the arrange- 
ment or lay out of the various parts. Upon this lay out, 
also, may depend the character of the forms, so that this is 
an additional requirement for its being made first. The 
diagram shows, further, the number of the various elements 
of the group. As one illustration of this kind of drawing 
can be mentioned a layout for piping, showing the numiber 
of elbows, Tees, valves, etc. 

In a diagram the briefest indication of shape is given, 
and not infrequently special conventional foiTns are used to 
stand for the miore intricate actual forms. In piping, for 
instance, a valve is represented b}^ two short lines perpen- 
dicular to and crossed by each other, one perpendicular to 
the line of piping and standing for the entire valve, the 
other parallel to the line of the piping and standing for the 
handle. In electrical work, also, there is a very frequent 
occasion for diagraming, and a very common use of con- 
ventions. The particular forms that are used in any case 



126 Notes on Practical Mechanical Drawing 

depend partly upon the usage of the company for whom the 
dra^^ing is made. 

Again, as another illustration of the diagram, an outline 
of a machine may be wanted composed of the main lines, 
together with the usual center lines. Perhaps, in this, the 
relation of some of the moving parts is wanted. These may 
be represented by heavy lines coinciding with the center 
lines of the members for which they stand, as in a Corliss 
engine valve gear diagram. 

The diagram is the most comprehensive of drawings; 
next to it comes the assembly drawing of an engine, machine 
or mechanism. This shows, perhaps in several views, the 
projection appearance of the entire subject to be treated. It 
may not show all the features, or parts, only the principal 
ones; but it gives certain facts not available in any other 
way. It shows the size of the whole, the place for the 
different component parts, and the relation between these 
places, together with certain desirable chief dimensions. 
The minor features, as remarked, such as bolts, nuts, keys, 
set screws, etc., are left off. Perhaps their place will be 
indicated by center lines; perhaps, not even that. In fact, 
the assembly drawing may be more or less in the form of a 
diagram itself. 

The diagram and the assembly drawing are not always 
made, but the latter is quite apt to be if the subject is at all 
complex, and when, in particular, it is manufactured for 
the first time. The assembly drawing of parts of a subject 
also may be made. 

Next to the assembly drawing comes the details. These 
may be made together upon a sheet of details, or each may 
be made on a separate sheet to be more handy in the shops. 



Working Drawings 127 

Again, the details may be made for the different workmen, 
according to the process through which the parts are to be 
put. There are details, for example, for the pattern maker, 
the blacksmith, or the machinist. The dimensions put on 
these and the general treatment will be that of interest to 
the particular workman handling them. Sometimes, how- 
ever, the detail drawings are made complete enough in all 
respects to answer for the several above mentioned require- 
ments. 

Finally comes the bill of materials. This, of course, 
is, strictty speaking, not a working drawing, but it is a very 
necessary accompaniment of it. The bill of materials 
consists of a tabulation of the stock required, the number 
and character of the pieces needed. To be specific, it is 
composed of: (1) An identification mxark as a number, 
which, as before stated, may, by its denomination, indicate 
the material. (2) Name of the part. (3) Number of the 
pieces needed to make one of the entire subject. (4) Name 
of material, if the identification is not complete as above. 
(5) Further general descriptive matter, like pattern number, 
dimensions of the rough stock, method of casting, etc. In 
very small subjects it may not be made a separate tabula- 
tion, but written near the separate parts. In other cases 
it may be a tabulation in one corner of the sheet containing 
the pieces detailed. When very complicated drawings are 
dealt with, it may be accorded a separate sheet. It gener- 
ally indicates the number of parts needed for making one 
of the combined subject. 



128 Notes on Practical Mechanical Drawing 

50. The development and arrangement of working 
drawings. 

In beginning a set of working drawings of a subject 
w^hich is entirely new in design, it is quite likely that the 
small features will be designed first, and the assembly 
drawings of parts, or of the whole, made afterwards. So 
there can be no rule for the order in which drawings are 
made. 

The convenient arrangement of a set of drawings is of 
first importance, and it is something which only experience 
and knowledge of the business will give adequately. But a 
few fundamental principles may be laid down to start with. 

Differences in manufacture and in the subject control 
the method of development and arrangement. Principles 
cannot be laid down applicable to all cases. But some one 
problem may be considered somewhat in detail, and will 
serve to show how^ it is done. About the best illustration 
that can be taken is an academic exercise, a problem which 
would be given a student in drawing, a problem of making a 
set of working drawings of a furnished model. Let the first 
illustration, for example, be a simple steam engine. 

First, let us take a general survey. Determine the 
chief dimensions or size of the whole, and choose such a scale 
as is necessary to properly present the assembly drawings, a 
plan, elevation and end view, upon one sheet without over- 
crowding the sheet, or on the other hand, making it so small 
that the character of the subject is not readily seen. Next, 
take in turn the various parts, and make the necessary 
working drawings of each. It is best to take a survey of the 
size of the largest piece and of the smallest, and see of what 
size they can be conveniently made, for it is desirable that 



Working Drawings 129 

as few different scales be used as possible. Lay out the pro- 
jections of the larger pieces first, and proceed toward the 
smaller, then the next smaller, and so on. 

It can be seen that in the practical problem of designing 
a machine the details would be made first, and afterwards, 
the assembly drawing, partly to see that there was the proper 
fit among the details when put together. 

Second, as to details of construction: Before any 
drawing is done, a list should be made of all the features 
needing to be detailed, and the number and kind of views 
required of each. If this is made a written list, the scope 
of the work can be gotten better in hand, the room on the 
sheet or sheets can be planned for, and the scale adopted 
which is necessary to show^ the parts to advantage. 

It is not always feasible to use only one scale for a 
dra\^ing throughout. The one for the assembly views needs 
frequently to be a smaller one than that for the details. Biit 
the fewer scales, the better. There is no objection, however, 
to one for the assembly drawings, one for the larger details, 
and full size for the smallest features like keys, bolts and 
screws, etc. 

Next, the arrangement of the sheets should be decided 
upon. In practical work dift'erent sized sheets are used for 
the different parts of the subject; frequently, the assembly 
views will be made upon a relatively large sized sheet, the 
main details on a second or medium sized sheet, and the 
smallest parts on small sheets. Small parts require, gen- 
erally, finishing or machine work, and it is more convenient 
in the shop to handle the small sheets, mounted as they 
often are, on compote board, or some stiff backing, and 
varnished to preserve them. 

(10) 



130 Notes on Practical Mechanical Drawing 

In the academic problem, it is sufficient to use the same 
sized sheets for everything, and use only the number that 
will show up all the parts advantageously. 

If the assembly views can be shown well enough in 
small size, they may be made upon the same sheet with the 
principal details. To get the best arrangement of views on 
a sheet, a free hand sketch treatment should be used first, 
that is, to an approximate scale, sketch roughly, by very 
light lines, the space to be occupied by each and all of the 
views. This will permit of an adjustment in the arrange- 
ment, if it does not at first promise to be good. 

Next, it is best to begin the careful drawing of the 
details first, leaving the assembly drawings until later, as 
the best interpretation and accuracy can be reached in 
working the assembly from the details. 

Draw the views of the bed of the engine first. Do not 
begin at the top or bottom, and build steadily down or up 
until finished, but lay out the chief, or the over all sizes, then 
the next smaller, and so on, to the smallest parts last; also, 
drawing not one view at a time, but the several of the set ; 
the same feature recurring in the several views should be 
treated in them all so that there should be harmony of parts. 

If a view can be developed by projection from another, 
it is better to do so than to use the scale and lay it out 
independently, for it saves time. But the scale relation 
must be kept in mind and discrepancies noted. 

It will be found, perhaps, that the drawing of one view 
will suggest the forms of the others, or show errors, if there 
should be such. Accuracy of form is of paramount imipor- 
tance, and anything that conduces to accuracy is in order. 
It is also certain that, since the various details are related 



Working Drawings 131 

to one another, where possible, lay out the chief sizes of 
them, so that this relation may be kept in view. In other 
words, it may be quite possible, in some subjects, to develop 
all the details together, more or less simultaneously, and 
where this can be done it is to the advantage of the drawing 
in accuracy. Where there are dotted forms, no distinction 
need be made from the solid outlines, etc. They may be 
done at the same time, and they may really help in the 
development of the forms, by checking the sizes of things. 

The matter of treating the larger features first, then the 
smaller, and so on, is of such importance that a few further 
directions about it are in order. The small things depend 
so directly upon the larger, that if the larger are drawn first 
there is more chance that the smaller will be right. Or, if 
done in this way, the process is logical in the same way that 
if a line is to be divided into a certain number of parts, say 
12 in free hand drawing, it is easier to divide it into two 
larger parts, then these two into two more each, and lastly, 
each of these into three. Very often some of the smaller 
features have very accurate requirements, whereas, the 
larger may not, for the former may be centered openings, or 
fitted parts, whereas the latter might be the over all sizes 
of castings which can vary one way or the other in size. 
Hence their size and location, if the former, can be more 
accurately ascertained after the larger features have been 
laid out. 

After the engine bed, draw the cylinder, the fly-wheel, 
the connecting rod, the eccentric and rod, the bearings, the 
main shaft, the valve gear, if any, and so on, leaving for the 
last, the bolts, screws, keys and minor fastenings, etc. 

As to the place on the sheets for the different views, a 



132 Notes on Practical Mechanical Drawing 

certain logical sequence and legibility should be observed. 
Large details should be put on a sheet by themselves, or 
else either along the upper part of the sheet, or at the left 
hand side. The next smaller parts should be put below the 
first, or to the right, and so on, so that the smallest parts 
are shown along the bottom, or along the right hand edge 
of the sheet. If it was a new machine, built for the first 
time, it is likely that for convenience to the workman in 
determining fits and locating related parts, assemibly details 
would be used. That is, the connecting rod, for illustration, 
would be shown complete in the upper part of the sheet, and 
its various component parts detailed in order below this. To 
be complete in explaining new forms, a bill of materials 
should be written alongside of the assembly detail. 

Related parts may be in projectively, related positions, 
provided the subject admits of it, or while not in projectively, 
related positions they may be so intimately related on the 
drawing that the connection is apparent at a glance. For 
illustration : A connecting rod — showing the rod at the top — ■ 
may have the straps to the left and right of the rod as if they 
had just been slipped off, their center lines coinciding with 
that of the rod ; the brasses may be shown also to the right 
and left of the straps as if they had been removed by simply 
sliding along their center lines coinciding with that of their 
position in the straps; finally, the keys, and bolts, etc., m.ay 
be put in the lower part of the sheet in any convenient 
place, arranged so that the left hand bolts, etc., belong at 
the left hand end of the rod, and those at the right, to the 
right hand end of the rod. This may be seen in part in 
diagram in Fig. 36. 



Working Drawings 



133 




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U LI 


u 


J 



C) 



LJ 



[U 



m 



^ 



3 



^ 



} 



m 



T 





[J 



El 



[T 



II 






_7 



Working Drawings 135 

Another logical and perhaps better arrangement is 
shown in diagram, in Fig. 37. Here the principle is followed 
of placing parts of a kind together, disregarding their exact 
position in the subject. The straps of both ends are put 
together at the left, but the upper one belongs to the left 
hand end of the rod, and the lower one to the right-hand end 
of the rod, a certain convention of sequence which is quite 
comm.on. Similarly, the brasses are placed at the right 
with, again, the left hand brass above and the right hand 
one below. 

■ The first mentioned plan of arrangement is rather risky, 
unless the subject be a very simple one, and admits of it 
without sacrifice of legibility, for of course it would become 
confusing if there were many pieces to remove from one 
another. 

If the engine were complex, say triple expansion, 
probably the connecting rods would be put on a sheet with 
the eccentric rods, or other long turned members, the brasses 
all together on a sheet by themselves, and the straps also. 
Even here, however, the rods for the high pressure (H. P.), 
low pressure (L. P.), and intermediate pressure (I. P.), would 
follow each other down or across the sheet in a certain 
sequence, which would be the same as that on the sheet of 
brasses and straps, etc. It is evident that such an arrange- 
ment would aid materially in reading the drawings and 
finding what is wanted. 

If several parts of the engine are put on a sheet, the 
groups of drawings of them should be separated by a little 
more space than the several views of a part, so that the 
identity of the different things is not confused. 



136 Notes on Practical Mechanical Drawing 

Where the projections of related parts cannot con- 
veniently be projectively related on the drawing, they 
should all line up to an imaginary limit. For illustration, a 
series of bolts of different sizes may be placed side by side, 
and the under sides of all the heads in line; this will show 
at once the size of the bolt, for the length under the head 
is the usual dimensioned length. 

The small adjuncts to component parts of a subject, 
like bolts, fastenings, etc., may go with the parts to which 
they belong in the case, for example, in which the connect- 
ing rod is treated complete on a sheet by itself. But the 
best arrangement, perhaps, is to put these small parts on a 
sheet by themselves, especially where the same kind of thing 
recurs in various parts of the subject, and is not intimately 
related to one of the large divisions, like connecting rod or 
cylinder. 

Parts which have to be made upon the same miachine, 
or by similar processes, are often collected on a separate 
sheet by themselves ; for example, there may be a sheet of 
bolts alone, of screws, of forgings and of castings; but this 
is done only where a large number of parts are wanted, and 
where, moreover, processes of manufacture have become 
somewhat systemimatized. 

If it takes more than one sheet to make the set of 
drawings, keep each sheet as far as possible self-contained, 
even though on some sheets there may be waste room. The 
economy of space profits little, nor the even distribution of 
views over the sheet unless it can be done without any 
sacrifice. Do not, for example, divide up the small parts, 
bolts, fastenings, etc., and put some on each of two or three 



Working Drawings 137 

sheets, merely to fill tip clear space on the sheet and econo- 
mize in number of sheets. 

Thus, has been laid out a plan of arrangement for a set 
of drawings. But it must not be taken for granted, as before 
remarked, that all subjects can be treated the same way. 
The character of the subject, the extent of the manufacture, 
and a number of things modify the process one way or 
another. The accuracy and the legibility of a drawing are 
the chief things. That development which will lead to 
accuracy is the best. That arrangement which enables one 
to read the drawings without trouble, also, is the best. 
Usage dictates the sequence in a set of drawings so that this 
is accomplished. Other things being equal, then, the valu- 
able draftsman is he who can, with the least outlay of time 
and labor, produce drawings that will enable the construction 
to be carried forward with certainty and dispatch. He 
should be a master of the principles of projection, but not 
a slave to them. 

51. Dimensioning: 

To dimension a working drawing is to do the most 
important part of the work. Upon it depends everything. 
If the scale on the drawing and the dimensions do not agree, 
the latter are assumed to be correct and govern the men 
in the shop. All that the workman needs to know must be 
put thereon, either in dimensions or footnotes, the latter 
being equally as important as the dimensions. 

If a drawing is made of a machine already constructed, 
or that it can be repaired, it may be necessary to take sizes 
from the original. This should always be done with the 
foot rule and calipers, never with the scale. The scale 



138 Notes on Practical Mechanical Drawing 

should be put as close to the distance to be measured, as 
possible, and if it is not possible to get close enough for 
accurate work, then use the machinists' dividers, and apply 
them afterwards to the foot rule, not the scale, to get the 
size. The scale is a tool whose edge should be kept sharp 
and undented, and furthermore, free of any dirt or grease 
likely to soil a drawing. 

The machinists' dividers are used to ascertain sizes of 
flat surfaces , the calipers, inside and outside, are used to get 
the diameters of holes and cylindrical forms. After a di- 
ameter has been obtained with the inside calipers, one end 
should be set flush with the end of the foot rule. If con- 
venient, place both against a fiat surface. With the outside 
calipers, rest one of the arms against one of the end faces 
of the rule. These directions will facilitate the making of 
rapid measurements. The diameter of a. cylinder should be 
placed on the end view of the cylinder. 

While it is true that dimensioning is an accurate opera- 
tion, still the beginner must appreciate that some things 
will permit of only approximate dimensions. A knowledge 
of processes of m^anufacture will show that it is a waste of 
effort to measure everything to the thousandths of an inch, 
as some tight fits, of course, have to be. Rough castings 
cannot be measured to a sixteenth of an inch with accuracy, 
and there is nothing gained by trying it. Work that is to 
be machined may or may not require to be very accurate. A 
tight fit may call for accuracy to a thousandth of an inch, 
another kind to a hundreth. Discrimination should there- 
fore be used in dimensioning. As an illustration of the 
application of approximate and exact measurements, take 
a line of sub-divided dimensions, which lie, on the one hand, 



Working Drawings 139 

between a finished surface, and the other the end of a cast- 
ing. The last subdivided dimension at the casting end 
should be omitted, and in its place an overall dimension 
should be given. The man who makes the casting will get 
the measurements he needs, while he who does the machine 
work and finishing will get those exact sizes he wants, and 
neither will in any way hamper the other. 

The question of what to give in dimensions is an impor- 
tant one. It may be said that everything should be dimen- 
sioned. This is only true in a degree. Those dimensions 
should be put on which are needed in the various processes 
through which pieces are to be put in making. Some knowl- 
edge of these processes is therefore necessary before the 
matter can be handled skillfully. A few ver}^ general 
directions may be given here. 

In the first place all dimensions should be the final 
working ones, no allow^ance should be miade for shrinkage 
of castings, etc. 

The distance between chief centers, and if the subject 
is symmetrical upon a center line, the distances also of these 
centers from the center line is always necessary. They are 
among the most exact of the dimensions, for centers may, for 
example, involve fitting of parts bolted together, and unless 
the centers are right in both pieces fit is out of question. Be 
sure these are correct before putting in other dimensions 
depending upon them. 

The overall dimensions are, of course, needed in every 
case. The subdivided ones between depend upon the nature 
of the work which is to be done upon the particular piece, all 
the subdivisions may or may not be needed. It frequently 
happens that there are two or three main subdivisions, like 



140 Notes on Practical Mechanical Drawing 

the distances of the sides or ends of a piece from one or two 
important center hnes, and in addition the distances of other 
smaller parts from these center lines. Where such exist 
we have three classes of dimensions. They ought generally 
to be figured up complete in each case to the overall, if for 
no other reason than that each may be a check upon the 
other. Aside from this they may be needed in constructing 
the piece. The three sets should be rather close to one 
another, the overall the outermost, and the subdivided the 
innermost of the three. The relation between the three 
should be at once apparent. As an illustration of this, see 
Exercise 10. In the absence of any limiting conditions, it 
is a good safe working rule to put in subdivided dimensions, 
and to fill in to the overall. 

Judgment of manufacturing processes m.ust be exercised 
as to whether the radius or the diameter is the dimension 
needed in a particular case. A circle passing through a 
series of bolts radially placed requires the radius ; a turned 
piece or a bored hole demands the diameter. The latter is 
designated as, for example, a IJ^' bore. 

When a hole is bored to carry a screw it is designated 
as tapped, for example, for a If screw, the tool used in 
making it being known as a tap. Or, if it is a casting, the 
hole is specified as cored for a sufiicientl}^ smaller size to 
permit of its being tapped out to the required size. These 
have to be allowed for. If a hole is tapped for a bolt the 
drawing may or may not show two concentric circles to 
stand for the base and the crown of the thread. If only 
one is shown it will be the circle which specifies the diameter 
of the screw, namely, the crown of the screw thread. 



Working Drawings 141 

In this connection it nriay be explained that "to ream" 
means to finish a hole with a "reamer " for a very smooth 
close fit. "To bore" means imply to cut out with an 
ordinary boring tool, while a "core " means a hole made in 
a piece when cast, by inserting a piece in the mould which 
which displaces the metal, but is rendered very brittle in the 
making and falls out readily. 

The bolts to go into a tapped hole will, if standard, only 
require the size or diameter which may be specified as a 
dimension, or by a note to one side, the length under the 
head and the length that is threaded, the latter specified 
generally as a distance from the end of the bolt. If the bolt 
is not standard it will require in addition to the above 
dimensions the height and diameter of the head and number 
of threads per inch. If the end of a screw is rounded, the 
dimensions of the overall and the length that is threaded 
should be given to the corner and not to the extreme 
end. 

As before stated, notes should be given, which may be 
included in the bill of materials, or may be written on the 
drawing. If the latter, the note will state the material 
used, how each part is to be finished, and the number of 
pieces required. Special directions - pertaining to making, 
painting, shipping, etc., may even be given in notes; also, 
sometimes, notes pertaining to erection are added, like 
"These rivets are to be field driven." 

When bolt holes are spaced equally around a center 
upon a disc or a cylinder head, for example, a circle passing 
through all their centers, together ^Aith radial lines also 
passing through the centers, constitute center lines for these 
forms, and the radius of this bolt circle is given, and also the 



142 Notes on Practical Mechanical Drawing 

number of the bolts, or the angular distance apart may be 
given instead. 

It may here be noted that all holes should have center 
lines, even if only two short strokes at right angles to each 
other, cutting across the curve of the hole, and cutting each 
other at the center of the hole. Always make a dash of a 
center line, cut across centers of forms, and also have dashes 
cut the principal lines of the drawing. 

Angles, if specified, may be given in degrees, or by 
co-ordinates or by tangents, depending upon circumstances. 
If in degrees, an arc is struck from the vertex of the angle, the 
dimension line constituting this arc; if by co-ordinates, any 
two distances at right angles to each other are used, measur- 
ing from each other and the vertex of the angle ; if by tan- 
gents, it is the length of a perpendicular measured from a 
base which is one side of the angle of length one, measuring 
from the vertex of the angle. The measuring by co-ordinates 
is particularly useful for the pattern makers. 

When a surface is machined or finished, an f mark should 
be placed on that line of the view which represents it as a 
line, and not on that view which shows it as a surface ; more- 
over, the f should be placed on the line in such a way that 
the cross bar of the f cuts across the line. 

It is sometimes necessary to go farther and specify what 
kind of finish a part receives as file finish, grind finish, plane 
finish, which would be stated by a written note near the f. 

Special care should be exercised in measuring those 
portions of any detached pieces which are fitted to other 
parts. In general, all measurements should be miade from 
center lines, or from finished surfaces. 

A few scattered directions about dimensions : 



Working Drawings 143 

(a) Always show filleted or rounded corners, where an 
adjoining finished surface does not prevent and give the 
radius of the fillet, as its size may be important in adding 
strength to the angle. 

(b) Where a number of rivets or small bolt holes are 
in a right line, the dimensions concerning these should be 
written between the arrowheads of an overall. It should 
contain the number, size, distance apart, as well as the 
distance of centers overall. The distance of the end holes 
to the end of the piece should regularly be given. 

(c) Where a taper is required it should be dimensioned 
with the taper per foot of length. Occasionally it is specified 
by giving the dimension at each end of the taper ; where this 
is done the approximate taper ought also to be given. 

(d) The dimensions of boards and iron plates should 
be specified in the order of width, thickness and length, for 
example a board 14'^ x J'' x 8'^. The grain will be parallel 
to the 8'' edge. 

In regard to where to place dimensions, a knowledge 
of constructive requirements, and a draftsman's judgment 
are necessary to determine them. 

A drawing is made for the workman to follow, and it 
must give him the information he wants, and give it in a 
way which it is the least trouble for him to find. This, it 
will be found, by examiining working dra^^■ings, has resulted 
in a certain system in the placing of dimensions, which can 
only be fully appreciated by such an examination. 

In the first place, no open spaces should be left un- 
dimensioned which the workman is likely to want, neither 
should additions or substractions be left for him to perform. 

As to placing dimensions upon the inside or outside of 



144 Notes on Practical Mechanical Drawing 

a view, practice differs. Other things being equal, dimen- 
sions on the outside are to be preferred, but things are not 
always equal. If a view is large, and there is much small 
work in the interior, it is not practical to run long limiting 
lines across the view to reach the outside; it will confuse. 
Legibility should govern in this matter. Overall dimensions, 
if possible, should be given the preference of the outside 
position; diameters should be placed, where possible, dia- 
metrically of the part dimensioned, if this does not confuse 
by making too many lines. 

Subdivided dimensions should invariably be made 
continously on a line, unless it is impossible to find a place 
where the line can be run without interference. Occasion- 
ally, one or two subdivisions have to be removed slightly 
from the line, but in no case should they be moved far enough 
to prevent reading the whole line readily. 

Center lines should never be used for dimensions, no 
matter how near to them it may seem desirable to have a 
dimension placed. Nor should dimension lines cross one 
another, if it can be prevented. If it cannot, then neither 
dimension figures should be placed close to the intersection. 
Nor, again, should a dimension be written across a line of the 
drawing, or across a center of anything, no matter how in- 
significant. 

The common two-foot rule has undoubtedly been 
generally adopted for standard, and, therefore, when 
dimensions are under two feet they should be specified in 
inches. Two feet should be written 2'-^" , and so on. In 
some lines of work, boiler work, for example, dimensions of 
whatever size are given in inches, as 120 inches. 



Working Drawings 145 

If the drawing is a design, the dimensions should be put 
on about as fast as the forms are constructed, because at any 
time a preceding dimension may be needed to find a subse- 
quent one. And, furthermore, it is a check on what is needed 
for construction, for what is needed to size in making the 
drawing will be very likely required in making the thing for 
which the drawing stands. 

If the drawing is made from a model, as for study 
purposes, before mentioned, it is probably best to leave the 
dimensions until the last, as one thing to consider at a time 
leads to accuracy. 

In constructing a drawing, and in setting off measure- 
ments and subdividing distances, use the scale where possi- 
ble. Use the dividers or compasses only where it is un- 
avoidable. 

In dimensioning sectioned surfaces, as before mentioned, 
which should be avoided, if possible, leave a clear space 
unsectioned for the dimension' figures and for the arrow 
heads also. 

If, again, the drawing is made from a model, and the 
dimensioning left for the last, as directed, then the following 
system should prevail : (1) Start at the top of the original, 
and going down, note all those things requiring horizontal 
dimensions, and put the same on the views which will need 
them, or show them to best advantage. (2) Starting at the 
left, and proceeding toward the right, move similarly, re- 
cording the vertical dimensions. (3) Locate all radii, 
diameters and oblique dimensions. (4) Check everything 
by going over the whole subject again. These steps should 
again be subdivided into more. After locating something 
requiring a dimension, mark simply the place where it is to 

(11) 



146 Notes on Practical Mechanical Drawing 

go on the drawing, by either sketching in the dimension 
Hnes and arrow heads free hand, or with the rule. After the 
place and the full number of all dimensions are located, then 
the foot rule should be applied, and the value of the several 
dimensions ascertained and recorded. 

In inking such a drawing, i. e., one made from the model, 
the same procedure should be gone through with in dimen- 
sioning, except that the arrow heads should be put in first, 
and the dimension figures next. Nothing in the way of 
precaution to preserve accuracy in dimensioning can be out 
of place. The inking of the limiting lines for dimension lines 
should precede the dimension lines, for the same reason that 
the arrowheads should precede the figures. For, if the 
former are not done first they are apt to be overlooked. 

The practice is common in the better drafting rooms 
to give accurate dimensions in decimals and approximate 
in fractions. Structural steel drawings are dimensioned in 
decimals. When the dimensions are given in decimals, the 
inch or foot marks should be placed in front of the decimal 
to replace the whole number. Similarly, in case of dimen- 
sioning in feet and inches, and the inches are zero, or less 
than one, a zero mark with the inch sign over it should 
always be put in the inches' place, or a zero in front of the 
fraction. 

Dimension lines on drawings are usually not made of 
any particular convention of line, because they are so varied 
in length. Generally they are composed of several dashes 
when long, varying in length according to the distance to be 
dimensioned. Some drafting rooms use a solid line, but 
much lighter than any of the other lines of the dra vvi ^ -d 
in rendering in ink where blue prints are to be tnn ' '.^ 



Working Drawings 



147 



it, they are made in red ink with a Httle black mixed with it 
to render it opaque, and make it show on the bhie print as a 
very Hght blue line. 

It is better to leave a clear space in the middle of each 
dimension line for the dimension figures, rather than write 
them either above or below it, because where a series of 

Fig. 41 





Ff " 

2 - 6 
2-6 









dimensions are close together, it is difficult to ascertain to 
which dimension line a figure belongs. Although the prac- 
tice of writing a dimension figure above the line is common 
in structural steel work. 

But on the other hand dimensions should not be crowded 
between limits too narrow to receive them. The several 
ways of specifying linear dimensions are shown in Fig. 41. 
The several ways of specifying diameters and radii are 
also shown in the same figure. 

When a dimension is to be placed outside a form, 
limiting lines must be run to the form and perpendicular to 



148 Notes on Practical Mechanical Drawing 

the direction of the distance which is to be specified. They 
should be continuous hnes, running just a trifle beyond the 
dimension Hne, and to a point just a trifle short of the 
out Hnes of the subject, as shoAvn in the figure. They should 
be of the weight and the treatment of the dimension lines 
in Fig. 41. The foot and inch marks may be as shown, 
either way, but the upper of the two is the best because 
there can be no misunderstanding of the s^^mbol. The 
dash should always be put between the foot and inch 
figures, to prevent misunderstanding. 

The dash marks when used for the feet and inches 
should be distinct and easily distinguished from accidental 
marks. They should go above and to the right of the figures, 
be about one-eighth of an inch long, thick at the top and 
pointed at bottom as the writing pen would naturally make 
them with the spreading of the nibs at the beginning of the 
stroke. 

The arrow heads at the ends of dimension lines should 
be made with the writing pen, sharp and concave with the 
sides of the arrow at about an angle of 30° to one another. 
Care should be exercised to bring the point of the arrow to 
exactly the limit it is to accentuate. There is no serious- 
objection to having only one side to the arrow, although 
common practice usually shows the two sides. Where 
leaders are taken from, a point to a dimension, the line can 
either be ruled or made free hand, entirely according to 
preference. The neatest appearance is attained when it is 
ruled. 

The greatest of care should be exercised in making the 
figures of a dimension. They should be printed, not written 
hurriedly. Figures that are from one to one and one-half times. 



Working Drawings 149 

as wide as they are high are the best, because legibihty is at- 
tained more through an increase in width than by increase 
in height. Dimension figures need only be about one- 
sixteenth of an inch high if they are made sufficiently broad. 
They should not be varied in size in different parts of the 
drawing, or cramped in places where space is scarce. Ample 
room should be provided for them under all circumstances. 
Where fractions occur the fraction line should, be perpen- 
dicular to the line connecting the two figures, or in other 
words, horizontal when normally reading the figures. Recent 
practice puts the numerator exactly above the denominator 
and omits the fraction line. The position of the figures tell 
that it is a fraction. 

The fraction figures may be made as large as those of 
the whole number, but also can equally appropriately be made 
slightly less ; the minimum should, however, not be as small 
as -one-half the size of the whole numbers. A good working 
rule is to make them just a trifle smaller than the whole 
numbers. 

It should be noted that uniformity in all respects is one 
thing which makes a drawing look ^^'^ell; that is, all figures 
and letters should be the same height, the same thickness 
of line, and of style. The same is true of the lines of the 
drawing, as before mentioned. 

52. Working drawings may violate the rules of ortho- 
graphic projection : 

Working drawings, although based upon the principles 
of orthographic projection, in practice do not bear witness 
to implicit dependence upon them. Projection is the 
theoretical side, working drawing the practical application, 



150 Notes on Practical Mechanical Drawing 

and as practice modifies theory, always, so working drawings 
depart from orthographic projection when circumstances 
warrant. 

Custom has sanctioned certain practices more or less 
universal for making drawings more explanatory with less 
labor, while there are innumerable short cuts, etc., adopted 
b}^ different establishments, known only to the individuals 
having use for them. Some few of the general principals 
which may be followed will be here touched upon :* 

(1) "That in each separate view, whatever is shown at 
all should be represented in the most explanatory manner." 

(2) "That which is not explanatory in any one view 
may be omitted therefrom, if sufficiently defined in other 
views." 

(3) "The proper position of a cutting plane is that by 
which the most information can be clearly given!" 

(4) "It is not necessary to show in section everything 
which might be divided by a cutting plane." 

(5) "Whatever lies beyond a cutting plane may be 
omitted w^hen no necessary information would be conveyed 
b}^ its representation." 

The views necessar}^ to show a subject do not follow^ the 
conventional ones of projection, for if one view^ is sufficient 
to tell the workman all the facts, more are superfluous, for 
example, one view of a bolt is all that is needed when the 
bolt is standard. The certainty that the workman could not 
make an^^thing else from the drawings than the thing in- 
tended is the controlling condition. 

When two pieces differ only in being rights and lefts, it 
is usually not necessary to draw but one of them, making an 

* See McCord Mech. Draw. Part II, Page 3. 



Working Drawings 151 

explanatory note on the drawing that two are wanted, one 
right and one left. 

Sometimes, although rarely, a section and an elevation 
are combined on the one view by superimposing the lines of 
theelevation over those of the section. This saves one 
view. 

Sometimes it happens that lines come so close together, 
notably, on a small scale drawing, that if put in true projec- 
tion they could not be distinguished apart. One should 
either be left out entirely, or else both sepa^rated a little for 
greater clearness. 

In drawing gears, a few teeth, perhaps only one, are 
drawn out in full; the remainder are indicated by dotted 
circles for their crowns and for their roots, the pitch circle 
being a dash and dot line, or the usual convention for center 
line, or it may even be made a solid line. 

In sectioned views, continuity of material is not inter- 
fered with by the introduction of hiinor elements in the plane 
of the section. They are either left out or put in dotted. 

Sometimes in the drawing of one part of an object, 
which it is particularly desired to show, there are other parts 
connected with it which may be rendered in dotted lines to 
help show the connection of them all. 

And so illustrations may be multiplied, but it is not 
necessary to go farther. The different illustrations in the 
book will show some of the short cuts. Judgment and 
experience will open up others to the thoughtful draftsman, 
and he will even then occasionally find that there are oppor- 
tunities for him to improve en past experience. 



152 Notes on Practical Mechanical Drawing 

53. Relative value of tentative and exact processes: 

In paragraph 12, page 17, mention was made of the 
difference between geometrical and mechanical drawing, and 
the need for accuracy has been dwelt upon. A process which 
in itself is accurate would seem to promise accurate results ; 
the fact is, however, that sometimes the length of the process 
and the steps of construction to be gone through with, open 
the way to errors in greater number and more serious con- 
sequence than if approximate cut and try methods were 
used. That is, each step in a geometrical process may yield 
a very small, and, in itself, negligible error, but in the aggre- 
gate, the several steps may make an error that cannot be 
neglected. Again, the construction by geometrical methods 
being accurate in theory, begets confidence in the draftsman, 
and he is apt to depend upon it and not to use his eyes in 
detecting errors. Now, the unaided eye is a most accurate 
instrument for discovering discrepancies, and if it is trusted 
it will prove an invaluable aid in truing up the drawing. 

Of course, the results decided as accurate by the eye 
must be proven out by measurement before they can be 
accepted as accurate. 

To take a couple of examples of these: (a) To find 
the center of a circle of given diameter, in other words, to 
bisect a line, strike an arc of estimated half to intersect the 
diameter, and with center each end of the diameter; this 
wilt leave a space to be further halved in correction, and so 
on. By adjusting the radius a couple of times or so, as 
accurate a center can be found as is needed, and more rapidly 
than by geometrical method. 

(b) By a similar method a line m.ay be divided into a 
given number of equal parts. By striking an estimated 



Working Drawings 153 

unit, a residue will be left which has to be divided into as 
many parts as the hne. By adding an estimated division 
to the first unit, another try m^ay be made, and generally, but 
two or three trys are necessary to arrive at quite accurate 
results. 

Practice and experience will show the opportunities for 
application of approximate methods, and dictate the wisdom 
of using them. As the draftsman's eye becomes trained to 
estimate distances, he can depend m.ore and m.ore upon 
approximations. 

54. Checking drawings: 

After a drawing is made, a bird's-eye Adew of it is not a 
sufficient means of checking it. The checking for accuracy 
should be done by methodical steps. Broadly speaking, 
the dra^^ing should be checked through the duplicate of 
steps by which it was originally made, and each step should 
be carried carefully throughout before the next step is 
undertaken. The folloAving is a good series of steps. 

(1) Identify every piece of a subject to see if all are 
fully shown, and to see if the requisite views of each are given. 

(2) Note lines of various views for completeness and 
correctness. 

(3) See that all dimensions are given that are needed, 
also working notes. 

(4) Scale every dimension to see if it is correct, putting 
a check mark alongside of each as checked. 

(5) See if they correspond with each other in dift'erent 
parts, in the assembly and the details. 

(6) See if arrow heads are anywhere missing. 



154 Notes on Practical Mechanical Drawing 

(7) See if dimensions are well placed. 

(8) See if accents for feet and inches are all correct, and 
fractions or decimals plain. 

(9) See if center lines are all in and correctly shoAvn. 

(10) Finally check for supplementary notes and di- 
rections, including bill of materials, if there is an}^. 

As a draftsman continues to work on a drawing, becom- 
ing more and more accustomed to it, his sense of its deficien- 
cies is apt to become somewhat dulled, hence checking is 
often done by another man, perhaps, two, to make doubly 
sure of the results. The final checker may be a man who 
does nothing else, and who is held responsible for the results 
after the drawing leaves the drafting room. 

These directions are subject to modification according 
to the particular class of work dealt with. Possibly the 
machine designer, for example, ma}^ need to still further 
check for interference betw-een different parts, "proper 
clearances," that bolts, screws, pins, and keys are standard," 
etc. 

55. Conventions in common use in working drawing: 

There are a number of conventional methods of repre- 
senting forms and certain construction, w^hich recur very 
frequently in working drawing. 

When a long thin member like an angle, or T bar, or I 
bar, etc., is broken for any reason, the approximate shape 
of the section is shown on the end. Sometimes the accurate 
shape is given so that one view^ may do for two. See Fig. 42. 

A round shaft or rod is broken, as shown, and if hollow, 
the approximate thickness of the metal is indicated. The 



Working Drawings 



155 



curve of the break may be put in with the curved rule, but 
it may just as well be shoAvn by free-hand treatment with 
the writing pen and with saving of time. Wood is shown by 
representing the splintering that is apt to accompany a 
break. 

Now and then colors in very pale tints are used to repre- 
sent various materials of construction. They ought only 





to be put in drawings which are stretched to the board. The 
following are the most important of these : 

Cast iron, Payne's grey. 

Wrought iron, Prussian blue. 

Steel, Prussian blue with tinge of carmine. 

Brass outside. Gamboge. 

Brass in section, Carmine. 

Grained or knotted wood, Burnt Sienna. 

Earth, Burnt Umber. 

Brick, Light or Venetian Red . 

Masonry, wash of India ink with tinge of blue. 



156 Notes on Practical Mechanical Drawing 

More natural effect can be given to other materials 
like wood, water, etc., according to the artistic skill of the 
draftsman. 

In some elaborate drawings a nice effect is obtained by 
shading, where possible, with the India ink lines and putting 
a tint over these of the convention for the material shown. 

Since the ability to put on a good flat tint is a necessary 
accomplishment of the civil engineer, if not for others, the 
following extracts upon the subject are quoted from F. N. 
Willson's Theoretical and Practical Graphics. 

"The surface to be tinted should not be abraded by 
sponge, knife or rubber." 

"The liquid employed for tinting must be free from 
sediment, or if the latter is present, it must be allowed to 
settle and the brush dipped only in the clear portion at the 
top. Tints, may, therefore, best be mixed in an artist's 
water-glass, rather than in a shallow receptacle." 

"Tints are best prepared from the India ink in cakes, 
and from other water colors in the pans. The size of the 
brush should bear some relation to that of the surface to be 
tinted." 

" Since tinting and shading can be successfully done, 
after a little practice, with only penciled limits, there is 
but little excuse for inking the boundaries; but if for the 
sake of definiteness, the outlines are inked at all, it should 
be before the tinting, and in the finest of lines, preferably 
of 'water proof ink,' although any ink will do, provided a 
soft sponge and plenty of clean water be applied to remove 
any excess that will 'run.' The sponge is also to be the 
main reliance of the draftsman, for the correction of errors 
in brush work ; the water, however, and not the friction, to 



Working Drawings 157 

be the active agent. An entire tint may be removed in this 
way if it seem^s desirable." 

"When beginning work incHne the board at a small 
angle, so that the tint will flow down after the brush. For 
a fiat tint, start at the upper outline of the surface to be 
covered, and, with the brush full, yet not so as to prevent 
its comiing to a good point, pass slightly along from left to 
right, and on the return carry the tint down a little further, 
making short, quick strokes, with the brush held almost per- 
pendicularly to the paper. Advance the tint as evenly as 
possible along a horizontal line; w^ork quickly between 
outlines, but more slowly along outlines, as one should never 
overrun the latter, and then resort to ' trimming ' to conceal 
lack of skill. It is possible for any one, with care and 
practice, to tint to, yet not over, boundaries." 

"The advancing edge of the tint must not be allowed 
to dry until the lower boundary is reached." 

"No portion of the paper, how^ever small, should be 
missed as the tint advances, as the work is likely to be 
spoiled by retouching." 

" Should any excess of tint be found along the lower 
edge of the figure, it should be absorbed by the brush, after 
first removing the latter' s surplus by means of blotting 
paper." 

"To get a dark effect, several medium tints laid on in 
succession, each one dr3dng before the next is applied, give 
better results than one dark one." 

" A tint will spread much more evenly on a large surface, 
if the paper be first slightly dampened with clean water. As 
the tint will follow^ the w^ater, the latter should be limited 
exactly to the intended outlines of the final tint." 



158 Notes on Practical Mechanical Drawing 

56. Tracings : 

Quite usually blue prints are made from which to 
manufacture things. Tracings or tracing cloth are the best 
for this purpose. The drawings may either be made on m.a- 
nila or detail paper, as it is called, or they may be made 
directly upon the rough side of the tracing cloth, as before 
mentioned. 

A few directions are necessary upon the handling of the 
tracing cloth, for it differs quite a little from paper drawing. 
The penciling, as Avell as ordinary dirt and soil, can be 
cleaned off by rubbing with gasoline, ether, benzine, or any 
highly volatile substance. Before inking on the cloth a 
little chalk should be rubbed over the surface with a rag, for 
there is more or less grease apt to be present, and it interferes 
with the drawing of lines in ink. If the fibres should get at 
all torn or injured, they may be repaired, partly, by rubbing 
with soapstone or hard beeswax. The soapstone comes 
convenient in the form of the soapstone pencil. 

Special care has to be noted in inking on the cloth, 
particularly if the smooth side be used. If it is a very pol- 
ished surface, the lines made by the pen are apt to be thicker 
by spreading, the ink flows out much more readily and con- 
sequently blots are easy to make. The precautions to be 
observed are to carr}^ less ink in the pen, than if working on 
paper, and to be sure that lines are dry before working up 
against them. Speed in crossing a line, or working from and 
to lines, is necessary. ]\Iistakes, as before mentioned, are 
not so easy to correct, hence care should be taken that no 
errors occur. 



Machine Sketching 159 



CHAPTER V. 
MACHINE SKETCHING. 

57. Machine sketching: 

One of the most important accomplishments an engineer 
can have, and one which, unfortunately, is somewhat 
slighted, is the ability to make a free-hand working drawing 
sketch. It is of constantly recurring usefulness for him to 
be able to do this. The machine designer finds it invaluable 
beyond a question, and, particularly, if he is able to do it 
well enough to turn his sketches over to the junior draftsmen 
to work up. The junior draftsman finds it valuable if a part 
of a m^achine has to be repaired, and temporary drawings 
made of it, or again, to make a record of construction for 
future reference. Frequently apparatus has to be stand- 
ardized ; this can be done readily from sketches. If a record 
of am^hing has to be taken hurriedly, to be later worked 
up, the sketch is also invaluable. To quote a very clear 
statement of the case from C. W. McCord's Mechanical 
Drawing : 

"It is supposed by some that deft handling of instru- 
ments of precision alone is required of the mechanical 
draftsman. This, however, is an error; no matter how 
expert he may be in the execution of working plans by rule 
and compass, the measure of his accompHshments is not 
yet full if he lacks the ability to make good free-hand 
sketches." 



160 Notes on Practical Mechanical Drawing 

"To the designer of a new machine of any degree of 
complexity, a fair degree of skill in this direction is absolutely 
essential. He may have the clearest, possible conception 
of the relations of the parts and of the general arrangement 
of the whole, but without some visible record of that con- 
ception, to which reference can be made from time to time, 
he cannot proceed Avith any certainty of success in the 
elaboration of details. This record is in the nature of a 
sketch, though not necessarily wholl}^ free-hand. Some- 
times certain absolute dimensions are assigned as a basis, 
such, for example, as the bore and the stroke in a steam- 
engine." 

"Or, again, definite movements must be provided for, 
and their elements reduced to settled proportions, as a 
preliminary; the resulting diagram forming the skeleton of 
the proposed structure. In either case some use of scale and 
instruments is, of course, proper, not to say necessary; but 
the filling out of this skeleton into the complete body is 
largely dependent upon free-hand work." 

"Usually this dependence is direct, the designer at once 
sketching in the general arrangement, for the sake of having 
something before him as a guide in subsequent operations." 

"In simple cases, however, he may proceed without 
this, to construct the details, adding them successively to his 
skeleton drawing, as each is completed. * * * In designing, 
then, perhaps the skeleton plan may indicate certain pins, 
which must be connected by a link; it may locate certain 
journals, and these miust be supported by a frame \\ith 
suitable bearings ; it may give the position of certain orifices, 
which are to be joined by pipes with valves ; and so on, in an 
endless variety of conditions and requirements. * * * Some- 



Machine Sketching 161 

times tentative methods are necessarily adopted, and in 
most cases there is a choice of ways and means, so that a 
judicious selection can be made only by comparison; in 
either event the utility of reasonably accurate sketches is 
self-evident, and from the nature of things it is equally 
apparent that they can be made most advantageously with 
the free hand, whether for the use of the maker, only, or for 
submission to the inspection and decision of another." 

"Not only are the sketches directly made use of for 
their special purposes, but in the very process of making 
them and the necessary measurements, the habit of close 
observation is cultivated, and, in addition, impressions of 
relative, if not of absolute dimensions, insensibly fix them- 
selves in the mind, and Avhat may be termed a sense of pro- 
portion is developed, which, to the d^esigner, is of the greatest 
value." 

The principals of free-hand sketching, however, are so 
apparently different from those of mechanical drawing, that 
it is difficult for the beginner to harmonize the two. 

We will take up the discussion of free-hand sketching 
by considering several classes of problems in which it enters 
and which are likely to meet the student in practical work. 

First, to make a complete set of working drawing 
sketches. It may be the designer's problem, before men- 
tioned, or it may be such a problem as discussed in the mak- 
ing of a complete set of working drawings. For the purpose 
of being able to set forth clearly a method, let us take a 
similar problem to the latter, that is, assume a set of working 
drawing sketches are to be made of a furnished model, or of 
a machine in the original. 

(12) 



162 Notes on Practical Mechanical Drawing 

These sketches may go upon the pages of a note book ; 
it is not Hkely the same care in laying out sheets and grouping 
of related views will be made as for the regular working 
drawing. The same planning of necessary view^s, however, 
"is required before any sketching is done. 

Each Adew may be treated separately as was outlined 
for the working drawing, or where several related views are 
to be considered, they can be develojped in the sketching 
even more advantageousl}^, in fact, it is best in every case 
to take the several projection views of a piece and develop 
them together. A certain harmony of relation exists, w^hich, 
in the absence of scaling, can be treated in no other w^ay as 
well. 

A particular scale is not generally a requirement in 
sketching, but the proper proportion of each idew and their 
sizes relative to each other is, and this is one of the chief 
requisites of sketching. 

Now let us make some observations about sketching in 
general, and as related to working drawing. A drawing is 
the record of the approximate relations of things, the relation 
of width to height, of the length of one line to the length of 
another, and so on. In setting down a value, it is to be 
observed that as one value in the subject is to another so 
should be the relation of the same two values upon the 
drawing. It is a proportion then of four members. 

The fundamental value or data in beginning a sketch 
may be taken as anything desired; then vipon it depends 
everything else drawn. That is, the length of a subject on 
a sketch may be assumed at will, and the width of it to be 
correct must be a certain size in comparison. The length 
and width over all having been ascertained, these can be 



Machine Sketching 163 

taken as units for comparison with other sizes, and so on ; as 
values become estabHshed they furnish the basis for the 
estimate of other values. The correctness of the sketch, 
then, is the correctness of the relations of the various values. 
Whatever helps in the establishment of correct values most 
readily assists the expeditious development of the sketch, 
and herein lies the problem of the draftsman. How can 
values be most correctly and expeditiously obtained? If 
small things are developed from the larger, this will be aided 
more than if the larger are derived from the smaller. As has 
before been mentioned, when dividing a line into a certain 
number of parts it is easiest to divide it first into halves, 
these halves into halves, making quarters, etc. This is not 
only expeditious, but if one size is taken wrong it does not 
affect all the others, as would be the case if a unit were 
stepped off the required number of times into the total 
distance to be divided. 

The principle used in dividing a line is the same one as 
that ^^hich should be employed in making the whole drawing. 
The small valu.es should not be treated first, but always after 
larger values upon which they depend. 

Again, the method of getting any one value and in 
handling the pencil is characteristic of free-hand drawing. 
The touch in free-hand drawing is very different, indeed, 
fromi that in mechanical drawing. In the latter, it is very 
firm and certain for the rule and scale, etc., to guide the 
pencil. The pencil should be sharpened to a long tapering 
and fine point. It should be held well back of the point so 
as to allow of greatest freedom of motion, and in the begin- 
ning, the miotion should be pretty nearly an arm motion 
with very little, if any, motion of the fingers. From the arm 



164 Notes on Practical Mechanical Drawing 

motion for larger values and forms, it should proceed to 
fore-arm motion for smaller values, and to wrist and finger 
motion for the smallest. 

Nor are values everything to be considered. Direction 
of stroke needs to be studied, and this quite as much as the 
former, is attained through the free handling explained. A 
working drawing demands a relatively, clean cut mechanical 
line for a finish line. A line in free-hand drawing is not ab- 
tained by drawing from one point to another with a steady 
continuous motion, as a line is made in mechanical drawing 
by the pen or pencil against the rule edge. Certainty of 
direction without such aids is impossible, and it can only be 
realized approximately by a step-by-step process. 

To draw a line, then, between two points the pencil is 
swung to and fro between the limits by a free arm motion, or 
fore-arm motion, if the distance is short, without making 
any visible record at first. It may be done by whatever 
holding of the pencil will give greatest freedom of stroke. It 
may be the arm will be held above the pencil point, may be 
below. When the motion of the arm seems to be guiding 
the pencil point fairly well between the limiting points, then 
a short record is made at these points, and then l)etween 
giving as a result a suggestion of direction, not in any sense 
a line. If this record happens to be very far out, it may be 
erased and another put in. It should be replaced, if it is not 
fairly suggestive of the true direction. Performing the 
same operation again, intermediate records can be made to 
fill out a little more the suggestion, resorting to a free arm 
or finger motion, if feasible, and distance is short. These 
records should be very light, barely visible. Skill in drawing 
implies a control of the pencil, and until the final hne is 



Machine Sketching 165 

needed there is no virtue in hard dark strokes'; on the con- 
trary, there is distinct disadvantage, for if they prove 
incorrect, they are hard to change. A line should be de- 
veloped, as described, by a series of approximations closer 
and closer to the desired line, and proceeding by stages that 
are similar. This ideal method of development is rarely 
realized in practice. After two or three approximations 
have been made it is customary to refine the line by going 
from one to the other, directly, making it by one final opera- 
tion as straight and black as desired. 

The principal precaution to be observed is to keep the 
preliminary approximations sufficiently light to permit of 
changes, if necessary, without spoiling the surface of the 
paper for additional lines. This can be done by cultivating 
and adhering to a light stroke ; as soon as the approximations 
become blurred they should be cleaned up or removed to 
make way for closer ones. 

The drawing of one line is not the only thing, however, 
to be kept in mdnd at one time. The relation of that line to 
all the other lines of the drawing is equall}^ important, and 
this may be realized in the following way : Carry all parts 
of a figure through the same stage as the line. Lay out the 
limits of a figure by short approximate strokes ; divide these 
limits into two or three of the principal subdivisions that 
suggest themselves by similar short approximate strokes, 
then proceed to smaller subdivisions and smaller in the same 
way. If subdivisions are not very apparent make arbitrary 
ones. Included as indicating subdivisions into parts are the 
center lines. It is a question in sketching whether the out- 
side dimensions and division — where apparent — into smaller 
forms should, precede the indication of center lines or not. 



166 Notes on Practical Mechanical Drawing 

The two ought certainly to go pretty close together. The 
principal center lines should, of course, be located first, then 
the shorter and minor ones, and all be preserved clear 
throughout to furnish landmarks for guidance. If at an}^ 
time through correction they should accidentally get rubbed 
out they should be put immediately back. They should be 
worked from in the sketch as they are in construction, the 
same is true of finished surfaces wherever they occur. Some- 
times a very broken up contour or group of forms may be 
simplified for preliminary treatment by circumscribing them 
by one or more simple forms, such as enclosing rectangles. 
After chief and minor subdivisions are made proceed to 
an approximate suggestion of form. But first check the 
results just obtained, in fact, check from step to step as 
approximations are made. As each new record is put down 
see that it harmonizes in every respect with all the other 
records made. As soon as a discrepancy is observed correct 
it by whatever change, upon careful survey, seems called 
for, in order to make it right ; even if it should reflect upon 
fundamental measurements. A constant watch upon the 
developing drawing and the correct relations of things is the 
way to proceed. And, of course, the more there is recorded, 
the more things there will be to compare one w4th another, 
and the more accurately can each value be estimated. Each 
is a unit of measures for the other. 

■ The first suggestion of the shape of the forms will tell 
much as to the truth of the forms. As each stage is com- 
pleted the general survey should be made making these 
comparisons. After this very brief suggestion of shape, a 
fuller one should follow and then a fuller yet, until forms 
appear well defined and clear as did the subdivision of 



Machine Sketching 167 

parts. So, stage by stage, each one of which is brief, the 
figures develop to completion. The accuracy of the drawing 
will depend upon the accuracy of the eye of the draftsman 
in making true estimates of the values and judgment in what 
is the important thing to be done at any particular stage of 
the drawing. It is not a straight-away mechanical opera- 
tion, but requires discrimination. 

The sketching of curved and circular forms will give 
trouble at first. Let us take a circle, for illustration, as the 
principles in treating all curves are the same. 

It is not to be expected that a circle can be sketched 
with anything like accuracy. Two records should be made 
at opposite ends of right angled diameters, then two more 
intermediate diameters estimated. These sketch records, 
if nearly right, should give a fair suggestion of the circle. 
Next swing the hand in the direction of a short arc, not as 
much as a quadrant, and when it is felt the hand is swinging 
right sketch in more strokes; do this with an arc diamet- 
rically opposite in each of the quadrants, thus getting, at 
each step, equal balance in all parts; then by the same 
finishing approximations complete the curve. If time is 
short, and rapid practical results are desired, a piece of paper 
may be used to lay off a few points around the center to act 
as landrmarks for the further work. Quite a good circle 
may be obtained in this w^ay. It shows up especially well 
when a number of concentric circles are to be drawn, and 
when pure sketch methods might result in indifferent circles. 
Irregular curves can be treated in the same way, and gener- 
ally, perhaps with better results, as we are not as famxiliar 
with irregular curves as we are with circles, and the same 
accuracy is not to be expected. 



168 Notes on Practical Mechanical Drawing 

To get the proper relation of values, i. e., distances and 
sizes of lines, a certain ratio must be obtained. The ratio in 
perspective drawing or picture making is a very different 
problem from that in mechanical drawing. In the former 
the ratios are between sizes that are not of certain true 
length, but apparent lengths due to the obliquity of these 
lines to the observer, or foreshortening, as it is called, while 
in mechanical drawing these are absolutely being the practi- 
cal lengths, as a rule, that are in the subject. 

Now in almost all cases a sketch, being but roughly 
approximate, and although in proportion, is not made to 
scale, else the actual ratio which one dimension is to another 
might be used as a basis for the ratio maintaining in the 
drawing. It is rather better for training in seeing propor- 
tions and values that this is not the case, that an estimate 
of the ratio of actual values be made and the drawing 
adjusted to it by sight, rather than measurement. 

Therefore, to obtain a value to record in drawing that 
is a ratio betw^een two quantities, estimate the value in the 
original by assigning either a numerical ratio of simple 
numbers easily transferred, or else, carry a conception of the 
ratio value in the mind without assigning any numerical 
value. For illustration, if a certain detail be one-fifth as 
long as the over all dimension, then that detail in the drawing 
should be one-fifth as long as the over all. In some cases of 
rather large subjects it may be advisable to make a space 
measurement of sizes for comparison. For illustration, if a 
certain detail is one-fifth the length of an over all, a pencil 
may be held up between the eye and subject, and covering 
one end of the detail to be measured w4th the end of the 
pencil, and the other end by the finger moved along the 



Machine Sketching 169 

pencil, this length may be compared with the over all by 
noting that it will go into it five times. Therefore, as the 
pencil unit is to the whole unit stepped off with it, so the 
detail in the drawing should be to the over all in the drawing. 
This method can be used where the quantities to be measured 
do not extend throughout a very wide range of vision, else 
the foreshortening, before mentioned, will cut a very serious 
figure and introduce inaccuracies. An eye estimate of values 
is better than an actual measurement made. After the 
drawing has all been made, however, its accuracy may be 
tested by these means very nicely. 

It takes consideralbe practice and a faithful adherence 
to the principles of drawing just laid down to sketch advan- 
tageously, but once learned, the accomplishment is invalu- 
able and finds usefulness in many minor ways in all drawing, 
even the mechanical. 

Sometimes sketching may take the form of a hasty 
drawing or drawings of a model from which afterwards 
working drawings can be made. It is possible, generally, to 
get the data into two or three views sufficient to work up at 
leisure into a complete set of working drawings. In fact, the 
problem is to choose the fewest views which will accomplish 
this result, and some discrimination has to be exercised to 
ascertain what they are. Or it may be that the final drawing 
is to be one which shows all the constructive facts — without 
being a working drawing — with the fewest views. Such a 
problem is illustrated by a patent office drawing. 

Sketching may be done upon regular sheets, but more 
frequently it is put upon scratch paper, or the pages of a 
note book. Use of a rule and compass is here not feasible. 
If done on the pages of a note book, the first problem is to 



170 Notes on Practical Mechanical Drawing 

adopt such a size that the subject may be treated properly 
and legibly. It may involve only one view on a page, or it 
may involve two or more. If there is room for more than 
one view on a page they should be sketched in the same 
projective relation to one another that they would be if 
mechanically drawn, and upon the different sheets of the 
note book, as far as possible, the views should be sketched 
in the same position that they would occupy, if drawn 
mechanically on a sheet; otherwise, a little confusion in 
reading the sketches may result. Where several views are 
to go on one page, in the sketching they should be roughly 
blocked out for proper allotment of space before doing 
further work upon any one view; where feasible, sketch 
them together throughout. 

In very rare cases a whole view even cannot be put on 
a sheet. It should be stopped at a conventional line, such 
as was described in the case of sections where the plane of 
the section moved from one place to another, and it is further- 
more best to sketch the two or more parts on the sheets in 
the same relative position so that, if called for, they may be 
cut along the line of their separation and fastened together 
to make the complete view. 

Views of parts should be. sketched as occupying the rela- 
tive position which they would in the machine. 

Some further practical points about sketching want to 
be kept in mind. 

(a) Throughout sketching, it is important to observe, 
carefully, right angles and the rounded corners; the latter 
may, in the preliminary operations, be made sharp, and only 
in the final stao:e rounded off to the desired amount. Be 



Machine Sketching 171 

sure that the right angles are always as near right angles as 
the}^ can be made. 

(b) Where forms are symmetrical upon a center or 
center line, sketch the two or more parts at the same timic. 
This plan of symmetrical development was instanced in the 
directions given for the drawing of a circle. No other sym- 
metrical form, should be treated in any other way. The brief 
preliminary record made upon one side should be followed 
by the same record on the other side, and as each stage is 
gone through with on the one, it should be followed by the 
same stage on the other. The mistake is quite comm.on to 
draw one side of thing that is symmetrical on an axis and 
then copy it faithfully on the other. It is ver}^ much more 
difficult to get symmetry in this way. 

(c) The sketches of a subject, if made from a model or 
the original, should be finished complete before any dimen- 
sions are put on, for the problem of sketching does not in- 
volve scale or absolute size, it is better if these are not 
considered. i\nd it is to be observed that the lines of the 
sketches should be much sharper and blacker if they are to 
be dimensioned, than if left without, for dimension lines and 
figures cover up form^. When sketches are ready for dimen- 
sions these should be taken from the subject in the way 
heretofore described for mechanical drawings, noting in 
particular to take only one dimension at a time; do not 
attempt to deal with more than one. 

(d) Sometimes sketches must be made hurriedly, when 
it is very important to subdivide the time to be used into 
parts to be given each to certain stages of the drawing. 
Roughly speaking, about as much time should be allowed 
for dimensioning as that for making the sketches. Again, 



172 Notes on Practical Mechanical Drawing 

the time allotted for sketching may be divided into parts, 
three of which to be given to the light preliminary work, and 
one part to finishing up in clear line, for the proportioning 
and the shape are more important than the character of the 
line. 

(e) If it should happen that time has been improperly 
allotted, or that a great deal has to be accomplished in a very 
short time, it may be disirable to cut steps short by leaving 
out certain things. Where parts are duplicated, for example, 
they need not be drawn but once. Where forms are en- 
countered which are perfectly understood, like wheels, only 
a small portion needs to be sketched. Much can frequently 
be omitted by giving a few written directions explanatory 
of them ; this is true of holes for bolts, fastenings of a similar 
character, etc. 

(f) Where forms are symmetrical upon a center line 
only one half needs to be sketched; where symmetrical 
upon a center perhaps only one quarter, a note being used to 
refer to the omitted part. But these short cuts to save 
work and time should be confined to the sketch, and not 
used indiscriminately in the working drawing. It is better 
to run the chance of being superfluous in the working draw- 
ing than to be insufficient, leading to mistmderstanding. 

(g) It very occasionally may happen that a complicated 
subject must be drawn in a very compact space, and in short 
time. There may not be room upon the pages of the note 
book to develop the forms, either entire or in separate parts, 
and even proper proportioning is not feasible. It may be 
necessary to sketch neglecting proportions entirely, or it 
may be convenient to change one dimension without chang- 
ing the other. Again, it may be that some parts can be 



Machine Sketchimg 173 

sho^vn in proportion, while others are not, compressing the 
drawing w^here needed to make it fit the space. These are 
practical problems that can easily be solved when they arise. 
With a knowledge of the principles of sketching, it becomes 
merely the question of recognizing the limiting conditions 
of the particular problem in hand. The draftsman who ex- 
pects to do comprehensive work cannot afiord to be without 
a knowledge of sketching. 

58. Blue print process and reproduction : 

A mechanical drawing made to be worked from is gen- 
erally reproduced by blue print, or analogous process. A 
drawing may be reproduced in photo engraving to furnish a 
cut for a catalogue. 

The following upon the subject of blue prints is taken 
from F.N. Willson's Theoretical and Practical Graphics : 

"A sheet of paper may.be sensitized to the action of 
light by coating its surface with a solution of red prussiate of 
potash (ferrocyanide of potassium) and a ferric salt. The 
chemical action of light upon this is the production of a 
ferrous salt from the ferric compound; this combines with 
the ferricyanide to produce the final blue undertone of the 
sheet ; while the portions of the paper, from which the light 
was intercepted by the inked lines, become white after 
immersion in water." 

"The proportions in Avhich the chemicals are to be 
mixed are, apparently, a matter of indifference, so great is 
the disparity between the recipes of different writers." 

The entire process, while exceedingly simple in theory, 
varies, as to its result, with the experience and judgment of 
the manipulator. To his choice the decision is left betw^een 



174 Notes on Practical Mechanical Drawing 

the following standard recipes for preparing the sensitizing 
solution. The ''parts " given are all by weight. In every 
case the potash should be pulverized, to facilitate its 
dissolving. 

No. 1. FROM LE GENIE CIVIL. 

SOLUTION. 

No. 1. Red Prussiate of Potash 8 parts 

Water 70 parts 

No. 2. Citric of Iron and Ammonia 10 parts 

Water 70 parts 

Filter the solutions separately, mix equal quantities 
and then filter again. 

No. 2. FROM THE U. S. LABORATORY, WILLETT'S POINT. 

SOLUTION. 

No. 1. Double Citrate of Iron and Ammonia . 1 ounce 
Water 4 ounces 

No. 2. Red Prussiate of Potassium 1 ounce 

Water 4 ounces 

"The solutions should be dissolved separately, as then 
they are not sensitive to the action of light. They should 
be mixed and applied only in the dark room." 

"The best American practice is to apply the solution 
with a fiat brush, and to obtain an even coat by. stroking 
first one way, then at right angles. If necessary, a coat of 
diagonal strokes may be given to secure evenness." 

"To copy a drawing, it is placed in a blue print frame 
made for the purpose, the sensitized paper, with the sensi- 
tized surface outermost and immediately back of the draw- 
ing. Exposure for about five miinutes to the rays of the sun 
is usually sufficient to get good results, after which the paper 



Machine Sketching 175 

is taken out and placed in a bath of water when the superflu- 
ous chemicals are washed off." 

"White lines can be drawn upon a blue print by using a 
solution of soda, potash, quick lime, or any alkali with 
water, adding a little gum arabic to keep the liquid from 
spreading. It can be applied with the writing pen, ruling 
pen or brush, according to the area desired to be white." 



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